Roadmap

This is the single planning contract for cleverly. It contains proposed work only. Implemented capabilities belong in the user guide, scientific contracts in the technical reference and DR-TMLE contract, validation results in evidence manifest, and cross-module standing decisions in the architecture invariants.

The main grid orders open work by beta milestone. Complete a milestone’s dependencies before its rows. An item enters the grid through one of the acceptance routes in Eligibility. An item that needs a new identification, regularity, or asymptotic argument stays in the future investigations grid.

cleverly is alpha, and it keeps no backward compatibility. cleverly.load warns with VersionMismatchWarning when a different version saved the artifact, and it does not migrate the artifact. This roadmap therefore carries no compatibility or migration items. The “Compatibility” section of CLAUDE.md states the rule.

This file lists open work only. A delivered row leaves the file. Code comments and evidence pages still name delivered rows, RM8 to RM33, by their IDs. The roadmap at commit 4ce96cda holds the record of each one.

The natural-extension review left the file when it was complete. The roadmap at commit 6a55f038 holds its questions, and the natural-extension verdicts hold its answers. The roadmap at commit 287a1fb5 holds the record of RM40, the DR-TMLE one-wrong inference correction. The roadmap at commit 2a8ad955 holds the record of RM39, the failure record and accounting of a study run. The roadmap at commit c1b2ce12 holds the record of X42, the applied tutorials for offers and pricing.

Remediation

This queue holds the remediation work that must be complete before a beta release. It holds shipped behavior that needs a correction or a recorded decision, and a published method needed to resolve a shipped refusal. Examples are wrong numbers, intervals that no claimed contract covers, capability rows that do not match their calls, late refusals, and shipped outputs that no registered study measures. The queue also holds a defect of the validation harness that can lose or invalidate a registered study run. Deliver the rows in priority order, and complete every row before the first beta release.

A new capability still needs its own contract and evidence, even in this queue.

No remediation row is open.

Each row takes a tier by the harm that its defect does to a user today. The table gives the tiers, from the most harmful. Inside a tier, a row with a wider reach comes first. A row that another row depends on comes before that row.

tier	reason	rows
a	a published number that is wrong, or that no derivation or read source covers. An anti-conservative number ranks above a conservative one	no open row
b	a crash, an exception that is not a refusal, a capability row that reads available and then raises, or an assessment that returns no report	no open row
c	a correct refusal that arrives late or as the wrong type	no open row
d	a diagnostic or a warning that misleads	no open row
e	a display or a message that misstates a fact that the fit records. By extension, an argument check or a capability row that misstates what a call accepts or needs, when no number moves and nothing raises that is not a refusal	no open row
f	an investigation, a declared design that moves no verdict, or a shipped output that no registered study measures	no open row
g	a published method needed to resolve a shipped refusal	no open row

A remediation row carries a priority below 1. The first decimal digit names a delivery group, and the second digit orders the rows inside it. A main-roadmap row carries a milestone instead. This project reassigns priorities and milestones when it re-triages the queue. The IDs and their anchors never change, so a commit names a row by its ID. A new row takes the next number that the history of this file has not used.

The red-cell ledger lists every red verdict that a registered study publishes. Red-cell owners names the item that owns each one. tests/unit/test_red_cell_ledger.py checks the ledger against the committed results. Each red verdict stays red under a reporting policy, so no verdict is hidden and no margin moves.

Main roadmap

Beta objective

The first beta makes cleverly a practical Python package for the effects of decisions made over time. One documented workflow answers each question in the table below.

question	required analysis
What happens if customers receive different sequences of offers?	static categorical regimen means and contrasts
What happens if the next offer depends on engagement?	prespecified dynamic categorical policies
What happens if prices are reduced at several decision times?	longitudinal continuous modified treatment policies
What happens if an offer is randomized with a specified probability?	known stochastic treatment policies
How sensitive is the result to modeling and weak support?	several estimators, support reports, and descriptive stability checks

The workflow stays CausalStudy -> identify -> estimate -> assess. Methods and policies attach to the causal question, not to a separate API for each implementation. Prespecified policies come first. Policy learning follows after honest evaluation is available.

This section is the plan for future work. The package already ships much of each milestone, and the user guide and technical reference describe that work.

LTMLE and SDR already fit static, dynamic, categorical, known stochastic, and modified treatment policies, including continuous treatment nodes. The package also ships clustered and cross-fitted longitudinal TMLE with the pooled update. It ships the cross-fitted longitudinal MSM, simultaneous bands over declared policies, and the full-refit bootstrap. The cross-fitted and cluster bootstrap kinds stay diagnostic. The rows below hold the open work only.

Milestones

The milestones order work by dependency and release role. Documentation, interface prototypes, and comparator preparation can proceed while an affected estimator is under repair. The milestones set scope, not dates.

milestone	deliverable	dependency	release role
B0	the acceptance policy, the status and refusal contract, and accurate refusals	none	the foundation for each beta claim
B1	the trajectory contract, the panel adapter, and evidence over longer horizons	B0	a reliable sequential core
B2	validated continuous longitudinal modified treatment policies	B1	required for the pricing beta
B3	sequential baselines and the two applied tutorials	B1; B2 for the continuous examples	completes the first beta. Both tutorials ship: sequential offers and sequential pricing. The former X42 row asked for a truncation curve in the pricing tutorial. That tutorial reads the support step in one sentence instead, and the owner accepts this
B4	categorical incremental policies and repeated longitudinal cross-fitting	the relevant B1 to B3 engine	the prioritized beta expansion
BP	the beta parity group: the former priority-1 rows that this reorganization does not place in B0 to B4	their own dependencies	required for the first beta
BD	the worked examples and the documentation, reviewed against the methods that ship at that time	every row of milestones B0 to B4 and BP, merged	the last work before the first beta
B5	honest learned-policy evaluation and selected production extensions	a stable evaluation engine	later beta releases

The first beta needs B0 to B3, BP, and BD. It does not need every estimator to support every policy, outcome, weighting, or dependence combination. It needs a usable path for each promised question, and honest boundaries for the rest. The release process sets the beta version. This roadmap does not change the package version.

milestone	item	readiness	dependency	details
B0	Experimental status and support rows	no new theory	none	RM42
B1	Longitudinal evidence over three to five decisions	published support; code shipped as experimental, studies pending	the shipped LTMLE and SDR	X39
B1	Longitudinal fitting options	no new theory; each option keeps its default bit-identical	none	X33
B4	Repeated cross-fitting for longitudinal fits	published support; pending source read	the shipped point-treatment repeats and trajectory-level splits	X46
BP	Repeated outcomes for SDR and IPSI	published support for the incremental case; a per-horizon reduction for SDR	the shipped LTMLE repeated outcome	X32b
BP	Adaptive-propensity IPTW	published support; pending source read	none	X21
BP	Plug-in omitted-variable limits with a declared parametric mechanism	published support; stacked-equation extension	the shipped plug-in bound	X26
BP	Per-arm outcome-adaptive C-TMLE intervals with a parametric outcome	natural extension candidate; parts (a) to (d) implemented	RM42; the shipped per-arm design	X58
BD	Worked examples for the shipped methods	no new theory	every row of milestones B0 to B4 and BP	X68
BD	Documentation review for new and changed methods	no new theory	every row of milestones B0 to B4 and BP; X68	X69
B5	Learned-policy follow-ups	published support for parts (g) and (h); natural extension for parts (i) and (k) to (o); published support; pending source read for parts (a), (b), (e) and (f); source audit for parts (c), (d) and (j)	the shipped learned-rule value	X11
B5	Longitudinal simulated-confounding replay with a time-fixed latent	natural extension	the shipped point-treatment replay	X48
after beta	Replicate-weight designs	source audit	weighted-law variance construction	X2
after beta	Efficient known-score ATT and ATC	published support; pending source read	the shipped known treatment mechanism	X35
after beta	Natural and interventional mediation effects	published support; pending source read	target-specific identification and evidence	X5
after beta	Continuous-time survival and competing risks	published support; pending source read	continuous-time intensity and targeting contracts	X6
after beta	Hazard targeting beyond a held baseline treatment	published support; pending source read	the shipped hazard targeting on a held baseline treatment	X70
after beta	Two-phase and outcome-dependent sampling	published support; pending source read	observed-data likelihood and influence correction	X7
after beta	Omitted-variable bounds on the other linear functionals	published support; pending source read	the shipped arm-axis bound	X9
after beta	Continuous-dose MSM with a second mechanism	source audit	implemented continuous-dose MSM targeting, missing-outcome arm targeting, and controlled-direct-effect targeting	X10
after beta	Fold-evaluated CV-TMLE with baseline strata	published support; finite-partition extension	the shipped fold-evaluated estimate and the shipped stratified fluctuation	X28
after beta	Simulated-confounding laws for point-treatment fits	natural extension; no new theory for part (d)	the shipped point-treatment replay	X47
after beta	E-value for a controlled direct effect	natural extension	the shipped E-value conversions	X49
after beta	Further DR-TMLE compositions	natural extension; no new theory for parts (d) and (e)	the shipped DRTMLE	X50
after beta	C-TMLE point estimates for further targets	natural extension; no new theory for part (f)	the shipped selector and outcome-adaptive paths	X51
after beta	Parametric C-TMLE intervals	natural extension	the shipped selector path; X58 for part (b)	X52
after beta	Missing-outcome CV-TMLE variants	natural extension; pending source read for the incremental and tilt axes of part (d)	the shipped stacked missing-outcome contracts	X53
after beta	Small-sample evidence for clustered intervals and boundary nodes	no new theory	the shipped clustered intervals and constant_node_plugin status	X54
after beta	Bootstrap extensions	published support; the book chapter of part (c) is not read	the shipped full-refit bootstrap; a HAL learner for part (b)	X55
after beta	Competing-event intervention targets	published support for part (a); source audit for parts (b) and (c)	the shipped censored LTMLE	X56
after beta	Joint intervention axes and tilt compositions	natural extension	the shipped single-axis fits and the MNAR tilt	X57
after beta	Long-horizon comparator parity for LTMLE and SDR	no new theory; comparator setup	the X39 studies	X59
after beta	Settings of the stacked and natural-course contracts	no new theory for part (a); natural extension for parts (b) to (d)	the shipped stacked and natural-course contracts; the shipped controlled direct effect for part (d)	X60
after beta	Fold targeting and fold evaluation	natural extension for parts (a) to (c)	the shipped fold-specific update and fold-evaluated report	X61
after beta	Other DR-TMLE and C-TMLE compositions	natural extension for parts (a), (c) and (d); no new theory for part (b)	the shipped DRTMLE and CTMLE; X50 part (c) and X51 part (a) for part (d)	X62
after beta	Missing data, intermediates and designs	natural extension for parts (a) and (b); no new theory for parts (c) and (d)	the shipped controlled direct effect and known treatment mechanism	X63
after beta	Intervention and policy declarations	natural extension for parts (a) to (d); no new theory for part (e)	the shipped intervention declarations	X64
after beta	Sensitivity analyses beyond the shipped scope	natural extension for parts (a), (b), (f), (h) and (i); no new theory for parts (c) to (e), (g) and (j)	the shipped sensitivity analyses; X61 part (c) and X63 part (c); a continuous natural-course mean for part (a)	X65
after beta	Simulated confounding beyond X47 and X48	natural extension	X47; X57 for part (c); X50, X51 and X62 for part (h); F5 for a continuous fit in part (f)	X66
after beta	Refutation and assessment adapters	no new theory	the shipped refute catalog	X67
after beta	Repeated outcomes for the sequential baselines	no new theory	the shipped LTMLE repeated outcome; X41	X71
after beta	Static regimen values from structural blips with time-varying features	published support for identification; the inference result is a preprint	the shipped StructuralNestedMean; the shipped LTMLE	X72
after beta	Assessment and study integration for the structural nested mean model	no new theory	the shipped assessment layer; the shipped StructuralNestedMean	X74
after beta	Studies of the targeting and fitting options	no new theory	the shipped stopping=, outcome_by_arm=, patience= and treatment_adjustment=	X76
after beta	Pooled-over-time parametric g-formula models	no new theory; the stacked equations of the shipped ParametricGFormula, with unit-summed scores	the shipped ParametricGFormula	X73
after beta	Data-tuned policies beyond the shipped tuned caps	published support for the shipped caps; source audit for the other tuned policies	the shipped data-tuned caps of modified treatment policies	X75
after beta	Censored data for continuous price policies	no new theory; Díaz, Williams, Hoffman and Schenck (2023) include censoring	the shipped continuous-node modified treatment policies and the learned censoring factor	X77
after beta	EP learner	published support; pending source read	shared study, fold, learner, and assessment contracts; a concrete analysis need	P1
after beta	Nested Riesz engine and initial catalog	published support; source audit complete	typed study, identification, result, and assessment contracts; a concrete analysis need	R1
after beta	Evidence-gated Riesz catalog expansion	source audit for each target	R1 and a target-specific derivation	R2

Rows in progress keep their order within a milestone. The BP rows close estimator gaps against the pinned comparators ctmle 0.1.2, ctmle3 0.1.0, tmle3 0.2.0, drtmle 1.1.2 and lmtp 1.5.4. They also close gaps against the survival packages survtmle, concrete and MOSS. X2 moves forward only if a pilot analysis needs survey weights. P1, R1, and R2 move forward only when they reduce a concrete implementation burden of a beta row.

Validate the claim that a release makes

Each released configuration has a support row and an evidence status that matches its output. Declare the supported configuration cells first, then choose the studies that cover them. Reuse existing evidence for unchanged components, and add checks for each changed construction.

check	purpose
an exact finite-law or analytic continuous-law calculation	verifies the intended functional independently of the estimator
influence-function derivative and remainder checks	verify the changed derivative terms and the stated robustness conditions
nonzero updates and deliberate mutations	detect mistakes that vanish under oracle nuisances
acceptable comparator runs	establish parity where appropriate, or give informative component and statistical comparisons with documented differences
end-to-end learned-nuisance studies	evaluate the user pipeline, not only supplied oracle predictions
repeated sampling	measures bias, coverage, SE calibration, and behavior under weak support
executable applied examples	verify the public workflow, messages, assumptions, and result persistence

When no comparator exists, the functional, derivative, mutation, and statistical checks carry the claim, as Theory and comparators states. Record comparator commits, dependencies, learner settings, supplied predictions, trimming, and variance conventions. Numerical parity and statistical performance are separate claims. When a study compares oracle mechanisms, add learned-mechanism evidence before a production-readiness claim. Keep historical results and preset margins, and publish failed or inconclusive results under the red-cell rule.

The first beta is ready when each statement below holds:

• the remediation queue is empty;

• B0 is adopted, and any known incorrect output or uncertainty is fixed or outside the supported claims;

• categorical LTMLE and SDR configurations, with paired effects and censoring where validated, carry evidence over three to five decisions;

• continuous longitudinal modified treatment policies pass their support checks and carry explicit support and identification assumptions;

• known stochastic binary and finite-category policies carry evidence over three to five decisions (X39);

• sequential g-computation and IPW are available over a declared subset, with correctly scoped uncertainty;

• both applied tutorials run through the public API and explain method choice and causal assumptions;

• the BP rows are delivered; and

• the code, documentation, distribution, and affected-study checks of the release process pass.

Future investigations

This grid is the research queue. Each row holds a claim that needs an argument of a new kind. Move a claim into the main roadmap when published theory supplies that argument, or when the Eligibility rule qualifies it as a natural extension. A missing comparator never keeps an item here, and a comparator never removes a stop. The hard-stop review read each earlier row under that rule. It moved each part that an established method or a natural extension carries to a main-roadmap row.

kind of missing argument	what it means
identification	a law or an assumption that identifies the target from the observed data
regularity	a pathwise derivative of the target, or a model in which the estimator is regular
asymptotic	a limit theorem for the estimator as the package builds it
adaptive-optimum inference	a limit law after a data-adaptive selection, or for a target with no fixed limit
arbitrary dependence	an argument for a fixed number of dependent units
serial dependence	a limit theorem for split-based TMLE under mixing
algorithm definition	a published definition of the procedure that the package would implement
efficiency	the efficient influence function of a model, and an estimator that attains its bound

investigation	kept claim	kind of missing argument	current boundary	details
Missing-outcome simulated-confounding replay	a replay of the stored estimator when the response or treatment-observation mechanism reads the treatment	identification	complete outcomes only. X47 holds a response mechanism that reads the covariates only	F12
Longitudinal simulated-confounding replay	censoring or survival outcomes; a time-varying covariate after the first treatment node; a time-varying latent with treatment feedback	identification	point-treatment results only. X48 holds one time-fixed latent on uncensored terminal-outcome fits	F13
Controlled-direct-effect simulated-confounding replay	the treatment axis on a fit with an intermediate	identification	fits without an intermediate only. X47 holds the outcome axis and an intermediate axis that holds the treatment	F15
Plug-in omitted-variable confidence limits	confidence limits of the plug-in \(E_n[\hat\alpha^2]\) for a learned mechanism other than the declared model of X26	regularity	the plug-in bounds, rv, max_bias, benchmark() and contour(). The one-sided limits and rva refuse under nu2_estimator="plugin". nu2_estimator="doubly_robust" gives them for any mechanism learner	F26
Targeted bootstrap inference	full-refit bootstrap consistency with data-adaptive or cross-fitted nuisances; a row-resampling (nonparametric) targeted bootstrap for learners other than HAL	asymptotic	the in-sample point-treatment TMLE bootstrap publishes its percentile interval, with a data-adaptive learner too, although the registered study measured only correctly specified nuisances. A cross-fitted point bootstrap, and every DRTMLE and CTMLE bootstrap, prints as a diagnostic. X55 holds the extensions that published support carries	F2
Longitudinal sensitivity-bound estimation	(a) a sample estimate of the bounds of Tan (2025); (b) its interval; (c) an omitted-variable bound or an E-value on a longitudinal fit	(a) asymptotic; (b) regularity; (c) identification	no sensitivity bound on a longitudinal fit	F16
Other refused C-TMLE and DR-TMLE compositions	C-TMLE ATT, ATC, incremental, modified treatment policies, the risk-ratio tilt, controlled direct effects, continuous doses and longitudinal functionals; DR-TMLE ATT, ATC, modified treatment policies, the risk-ratio tilt, incremental, controlled direct effects, longitudinal functionals, continuous doses, a partial guard with missing outcomes, fold targeting and fold evaluation; DR-TMLE combined with C-TMLE	regularity for the C-TMLE targets; asymptotic for the DR-TMLE targets	named pre-fit refusals. X50 and X51 hold the compositions that moved, and X62 holds the others	F5
Selector-path C-TMLE inference	inference after the shipped stopping-index selection; a fold-specific selection under cv_evaluation=True or targeting_scheme="fold"	adaptive-optimum inference	point estimates and path diagnostics. The greedy, ordered, discrete, lasso and learners paths refuse ci, pvalue and std_error, except a discrete fit whose one declared candidate is the full adjustment set and a learners fit with an empty declared list. X52 holds one declared partial candidate with parametric learners	F18
Outcome-adaptive C-TMLE generated-design inference	a flexible outcome learner; a nonparametric shared multinomial design; the cross-fitted construction; the fold average and a fold-specific update; local uniformity over the nonparametric model	asymptotic; regularity for the shared design	point estimates only, under the generated_design_plugin status. The per-arm study measured the diagnostic 8 to 24 percent too small (the applied revert). X58 holds the per-arm cells with a parametric outcome, and X52 holds the shared and composite parametric cells	F19
Other missing-outcome CV-TMLE variants	a cross-fitted DRTMLE with delta= or a missing treatment, and reduced_crossfit="nested" on the composite and on the randomized missing-outcome DRTMLE	asymptotic	the in-sample composite DRTMLE. X53 holds the TMLE variants	F21
Grouped cross-fitting beyond point-treatment TMLE	clustered C-TMLE intervals beyond the parametric cells of X52	asymptotic	C-TMLE refuses id=. X51 holds the clustered point estimates	F22
Time-respecting cross-fitting	blocked-temporal and rolling-origin folds for a dependent calendar series	serial dependence	iid and grouped cross-fitting only	F7
Learned-policy value outside the published conditions	an interval at an exceptional law; the full-refit bootstrap; a continuous treatment; a fold-evaluated DRTMLE learned rule; CTMLE with learned_rule=; a learned rule with missing outcomes or a missing treatment; an E-value for a learned-rule contrast	adaptive-optimum inference; asymptotic; regularity	LearnedRuleValue fits the fold-evaluated CV-TMLE of learned rules under the limiting-rule condition. Its boundary study measures under-coverage at an exceptional law. X11 holds the compositions that moved	F27
Inference at a boundary node estimate	an interval in the rare-event local regime, where the node hazard shrinks with \(n\)	asymptotic	the point estimate stands under the constant_node_plugin status. X54 holds the interval at a fixed law	F31
Finite-sample limits of clustered intervals	an interval below 4 clusters	arbitrary dependence	few_cluster_plugin from 3 to 9 positive-mass clusters, and to 19 for LTMLE, which shows a labelled \(t_{J-2}\) interval. no_cluster_variance_plugin below 3. X54 holds the measurements from 3 clusters up to those floors	F28
The ctmleGlmnet type-2 path	a type-2 candidate sequence and its fluctuation	algorithm definition. No published source defines the type-2 sequence, and the R code disagrees with itself	strategy="lasso" runs the C-TMLE1 construction only, and no keyword selects a type-2 path	F29
Fold policies that read the treatment or the outcome	outer folds stratified on the treatment or the outcome	asymptotic	unstratified folds, stratify_by="none", which is the default. A split that reads \(A\) or \(Y\) refuses before any learner	F32
Other intervention and design compositions	the composite missing-treatment indicator with a controlled direct effect; an IPSI plan with a modified-policy or risk-ratio-tilt node; an MSM weight from a learned mechanism; automatic cumulative-bound selection for LTMLE	identification; regularity; adaptive-optimum inference	named pre-fit refusals. X63 and X64 hold the declarations that a natural extension carries	F33
E-values beyond the total-population arm contrast	the ATT and ATC E-value on a binomial outcome; the E-value of a regime, policy or incremental contrast, with the derived risk ratio off the arm axis	identification	E-values of total-population arm contrasts, and the standardized ATT and ATC E-value on a gaussian outcome. X49 holds the controlled direct effect, and X65 the other sensitivity requests	F34
Inference for sequential baselines with data-adaptive nuisances	an asymptotic-linearity result for longitudinal sequential g-computation or IPW whose nuisances are fitted by a data-adaptive learner	asymptotic	the point estimate stands. A fit that reads a regression fitted by a learner other than GLM takes the adaptive_baseline_plugin status and reports a plug-in diagnostic only	F35
Locally efficient g-estimation of the structural nested mean model	an interval for the blips from the g-estimator that weights its instrument by the conditional variance of the outcome residual	efficiency	the shipped StructuralNestedMean solves the unweighted equation. Its interval is valid under the linear model, and it is not the efficient estimator of that model	F36

Eligibility

cleverly accepts established methods and natural extensions of established theory. Published support or a natural extension supplies the theory. An acceptable comparison with an existing implementation can then supply acceptance evidence for the claims it covers.

A natural extension is a bounded adaptation of known results. It needs a written statement of its target, assumptions, estimating equations, and inference. It does not need a separate published theorem for each composition. When the remaining work is such an adaptation, implement it.

Theory and comparators are separate questions. Theory and comparators is the repository standard for both. The absence of a comparator, exact or related, never blocks an item. Missing fundamental theory blocks the affected claim when a natural extension of established results cannot supply it. Defer that method, configuration, or inference claim, and keep every unrelated supported capability. Parity and related comparisons do not excuse a known defect or a misleading uncertainty estimate.

Three acceptance routes

route	sufficient justification	required evidence
established method	a published method covers the target and the proposed estimator	an assumption map, implementation checks, and scoped statistical validation
acceptable implementation comparison	a credible reference gives informative evidence for a method that the first or the third route already covers in theory	the documented target and algorithm differences, a reproducible reference, justified comparison metrics, and independent checks of each claim the comparison does not cover
natural extension	existing results extend through routine finite-dimensional or algebraic arguments	a short derivation of the changed terms, explicit assumptions, and tests that expose the change

A natural extension satisfies every condition in the table below. The natural-extension verdicts record earlier readings under this rule.

condition	what it requires
a published base	the extension starts from one published result, and it cites that result’s exact locator
an established argument	each step reuses the base result’s own argument, or a standard result. The next table lists the standard results
no new fundamental argument	no step needs a new identification, regularity, or asymptotic argument, and no source records a step as open or as a defect
inherited conditions	the remainder and rate conditions carry over from the base result, and the contract states each one
a written record	the item’s contract states the base result, each step, and the argument that carries it
its own evidence	each step that can vanish at the truth has a nonzero witness. An interval or another repeated-sampling claim also needs a registered study

Each step below counts as an established argument. A step of this kind needs no further source.

standard step	what it carries
linearity	a sum, a difference or a fixed linear functional of asymptotically linear estimates, such as a contrast, an attributable risk or a restricted mean
the delta method	a smooth function of a fixed number of estimates, such as a ratio, a fraction or a transform
a fixed-dimension stack	estimates that are each asymptotically linear on the same rows, stacked by Cramér–Wold, with their joint covariance from the stacked curves
the chain rule for influence functions	a composition of differentiable functionals, including a known weight or a known design
an indicator reduction	a binary-treatment result applied to \(1\{A = a\}\) for one arm, or to a composite indicator such as \(\Delta \cdot 1\{A = a\}\), when identification holds for that indicator
a finite partition	a marginal result applied inside each of a fixed number of baseline strata, then stacked
a finite categorical sum	a result for one category applied to each of a fixed number of categories, and summed with known weights that do not depend on the law. At one node, the weights can be known functions of the history at that node, such as a known stochastic policy. Over several nodes the step applies inside each node of the sequential regression, and the chain rule carries the composition
a fixed full-rank projection	a fixed working model, with known projection weights, projected over a fixed finite set of jointly asymptotically linear estimates, such as an MSM over declared policies. The derivative of the projection equation is nonsingular at the truth. Estimated projection weights add a derivative term and are outside this step
a cluster as the unit	an iid result applied to independent clusters as the sampling units, with cluster-summed curves
a stacked estimating equation	a smooth finite-dimensional nuisance whose score is stacked with the target equation, as Saul and Hudgens (2020) describe

Each adaptation explains why its assumptions and its remainder still apply. Apply the conditions to reach a verdict, not to find a reason to wait. When every step is in the table above, the burden falls on an objection: a source that records the step as open or as a defect, or a required argument of a new kind. Without such an objection, the extension qualifies. A reading that rejected an extension before this rule is open to a new reading under it.

An extension that fails one condition is new theory. It stays in the future investigations grid. These examples fail:

example	why it fails
inference after a data-adaptive selection step, such as an adaptively selected policy	no established argument carries the selection
a fluctuation fitted on each fold’s training rows in place of a pooled one	the update reuses the rows that fit the initial nuisances, so the held-out influence function is not mean zero. Upstream lmtp commit 9996b04 records this as a bug
a growing target dimension	it needs a limit theorem of a new kind
arbitrary dependence between units	no independent-unit or independent-cluster argument applies
the mean outcome when every unit takes one fixed value of a continuous treatment, in a nonparametric model	the target is not pathwise differentiable, so regular root-n inference does not carry over

No route accepts an influence function that omits a required term. An intervention law that depends on the observed law, such as a propensity tilt, adds a derivative term. A comparator that omits the term cannot justify its omission.

When a proposed algorithm needs new fundamental work, use an existing covered estimator of the same target where one exists.

Comparisons

An exact comparator is useful when one exists. Neither an exact nor a related comparator is an eligibility requirement or a universal release gate. Do not defer a capability only because no library implements the identical target, algorithm, fold construction, or composition. Use the strongest feasible comparison and state its scope. A comparison is acceptance evidence for the claims it covers. The evidence pages label each claim that rests on a comparison as comparator-backed.

A planned comparator run that has not finished does not block a method either. The method ships when its Python studies pass with their expected properties. Until the run finishes, the evidence names the property studies and carries the label “comparator runs pending”. A later change registers the comparator results and fixes each defect that they show.

comparison	appropriate use	claim it supports
matching implementation	the same target, and an aligned algorithm and settings	numerical parity within declared tolerances
different estimator of a shared target	TMLE, SDR, IPW, or g-computation under aligned causal assumptions	target recovery, and comparative bias, coverage, efficiency, or stability
related target or component	an overlapping binary case, a categorical reduction, a density-ratio component, or a projection	evidence for the shared component or reduction. Checks of the extension supplement it

Differences in learners, targeting, trimming, normalization, or finite-sample construction can be acceptable. Document their consequences, and choose metrics that suit the comparison. Agreement on a related target does not establish the full target. Validate the uncovered part through a written adaptation and independent calculations or studies. Reject a comparison whose differences make the claimed conclusion uninformative.

A comparator’s bug remains a bug when cleverly reproduces it. Where code and paper disagree, the published derivation governs, and the discrepancy becomes a nonzero regression or mutation test.

Record the comparator’s source revision when one is available. That record identifies what ran. It does not require an exact comparator method.

Classify the analysis and its inference

status	meaning	public behavior
supported	an acceptance route and its scoped evidence are complete	normal availability, with stated assumptions and coverage limits
experimental	the target is justified, but an algorithm or inference extension has unresolved evidence	no opt-in. The package returns the estimate and, where it can compute one, the interval, and each carries the label with its reason. An interval with no computable plug-in curve is withheld
unavailable	the implementation is absent, the request is invalid, or a known defect makes the claimed analysis unreliable	a refusal before fitting where possible, which names the reason and an available alternative

A supported point estimate does not make its confidence interval supported. Track support by the combination of target, estimator, outcome, weighting, splitting, and inference. A configuration that passed does not certify another configuration of the same method. The package reports the experimental label on every estimate, and RM42 owns it.

The readiness labels rate method support, not programming effort:

• published support: a paper derives the method and inference claim;

• natural extension: a published base and the standard steps above carry the method and inference claim;

• no new theory: the item reuses shipped estimators and adds no statistical claim;

• source audit: a published paper appears to cover it, but the exact construction must be matched and discrepancies resolved before implementation;

• waiting on published theory: related methods exist, but the requested composition or inference claim needs a new identification, regularity, or asymptotic argument that no bounded extension supplies; it belongs only in the future investigations grid; and

• pending source read: the governing result is identified but has not been read first-hand into this package’s contract.

Definition of done

An item is complete only when all applicable conditions hold:

• the estimand is registered and covered in both directions by the oracle and evidence gates in tests/unit/test_registry.py, with an evidence row naming which instruments check its influence curve and which mistakes none can see;

• every well-posed composition still refused has a pre-fit test pinning the refusal and message;

• signs, masks, guards, and counterfactual blocks that can vanish at truth have a nonzero witness or deliberate-mutation control in addition to exact-law checks;

• cross-module changes satisfy the architecture invariants;

• reader-facing behavior, methodology, references, and evidence are updated without presenting a proposal as a release claim; and

• every relevant check has run locally and GitHub Actions is green. CI is the final merge signal, not a substitute for the local validation record.

Red-cell owners

Each red cell in the red-cell ledger names its owner by an id in the table below. tests/studies/evidence/red_cells.py reads this table. tests/unit/test_red_cell_ledger.py fails on four states: a red row with no owner, an owner with no red row, an owner that the id column does not list, and a red row in a gated study.

Every red verdict is diagnosed first. A genuine problem (an algorithm defect, an inconsistent estimator, or a test or design bug) is fixed, and the study re-runs under a fresh declaration that states the change. A red cell with no defect stays red under reporting at its registered budget and margin, with an owner row below. No change may make a test less meaningful or easier to pass: moving a margin, adding replications to cross a bound, weakening the law, dropping or relabelling a cell, or substituting an oracle. The red-cell rule gives the full text.

The RM18- owners hold the cells that went red when sixteen registered studies moved to unstratified folds and bounded laws, and five longitudinal studies moved to the pooled update. A declared diagnostic read each cell once. Each diagnostic directory and its tests/unit/test_rm18_* test rebuild the reading from the committed rows. No reading names a defect in cleverly.

The strata-boundary-mean and band-finite-sample owners hold joint-coverage and calibration cells that a declared oracle-band diagnostic read as finite-sample. tests/unit/test_band_shortfall_reading.py rebuilds each reading from the committed rows. Like the RM18- owners, they are standing records of a reading. They do not gate the beta release.

The X20-bootstrap owner holds the bootstrap kinds that stay diagnostic. It does not gate the beta release either.

The X41-negative-control owner holds the three misspecification_control cells of the sequential-baselines study. They are a declared negative control and not a defect. On law X every main-terms GLM is wrong, so the rule must fail. No work is owed.

The F4-calibration-draws owner holds two cells that read one draw set of the multi-arm missing-outcome DR-TMLE study. It is a standing record of a reading, and it does not gate the beta release.

The composite-high-arm owner holds the ey[high] truth row of both implementations in the composite missing-data study. It is a standing record of a reading, and it does not gate the beta release.

The X16-plugin-variance owner holds the binary_lasso coverage row of the C-TMLE candidate-sequence study. Plain TMLE shares its shortfall on the same samples. It is a standing record of a reading, and it does not gate the beta release.

The F1-power-design owner holds the power cell of the known-policy study, whose declared size gives it an exact power of 0.5365. It is a standing record of a reading, and it does not gate the beta release.

The mtp-point-calibration owner holds one calibration cell of the point modified-treatment-policy study. Its standard error is conservative, and the diagnosis finds no defect.

The mtp-pricing-calibration owner holds the truth rows of the price study that read a standard error below the empirical spread at a finite size. The diagnosis finds no defect. The mtp-pricing-learned-density owner holds the learned-density cells of mtp-pricing, whose standard error is conservative. The X40-sdr-heavy-ratios owner holds the SDR cell of the boundaries study, whose standard error runs short. The package labels that interval experimental.

The X19-competing-calibration owner holds one calibration cell of the IPSI dropout study. Its standard error is conservative, and the diagnosis finds no defect.

The mtp-longitudinal-limits owner holds one cell of the longitudinal modified-treatment-policy study whose diagnosis finds no defect: a finite-sample calibration cell.

The F28 owner holds the clustered cells of the unequal-size and few-cluster studies that read red under their reporting policy. It owns a finite-sample limit, not a missing theorem. X54 is the work that closes these cells.

The X4-finite-sample owner holds one coverage cell of the SDR study at n = 2,000. LTMLE shares its shortfall on the same draws, so the diagnosis finds no defect in SDR.

The X45-finite-sample owner holds one calibration cell of the parametric-gformula study. The study declares the reading before its run, and the diagnosis finds no defect in ParametricGFormula.

The X8-logit-small-stratum and X8-identity-small-stratum owners hold cells of the two stratified MSM studies in their smallest stratum. Each is a standing record of a reading, and neither gates the beta release. The X8-drtmle-one-sided-bias and X8-drtmle-small-stratum owners do the same for the stratified DR-TMLE study.

id	work	acceptance
F18	an inference result for the shipped selector path	an influence curve derived after the stopping-index selection, and a registered study whose selector_necessity and type_i_error cells pass their existing margins at their existing budgets. The multi-arm interval_calibration/correctly_specified cell must also pass its band, because its standard-error ratio interval, 0.8987 to 0.9862, measures the fixed-candidate covariance that F18 replaces
F19	an inference result for the generated design, the red cells of ctmle-oat-per-arm, and the short-SE truth rows and ladder rungs of ctmle-oat-per-arm-strata-missing	a published result, or an Eligibility-qualifying natural extension, that establishes whether the ordinary adaptive-propensity curve suffices for the cross-fitted shared-multinomial joint target. For the per-arm design, a curve that adds the generated-design term \(c^\top \mathrm{IF}_\beta\), with \(c = E[(1 - g_0 / G)\, \partial \bar Q / \partial \beta]\), or a source that removes it. Implement any contribution the result requires, then register covariance and coverage evidence at declared budgets. The per-arm revert cells must pass their declared bands under a fresh declaration. X58 plans the per-arm part for the configurations that its support predicate admits. The committed red cells keep their verdicts and stay owned here. The generated_design pair stays a reporting diagnostic, and acceptance does not require a negative standard-error deficit
F27	an interval for the fold-average learned-rule value outside the published conditions	F27 gives the acceptance for each request. The exceptional row needs a published result. The weak_blip row is a finite-sample limit at n = 2,000 inside condition C3
RM18-fixed-weights	the interval_calibration/static__correctly_specified cell and the paired ey_regimen[never] row of weighted-ltmle-crossfit	reading finite-sample, contracting and equivalent at the declared budget (tests/diagnostics/rm18_fixed_weights/). The pooled update applies the weighted targeting equation, so the reading is no reason to revert it. A result for complex surveys, estimated or calibrated weights, clustering or other longitudinal weight laws is still open. Karim (2026), arXiv:2606.30918v2, is adjacent point-treatment survey theory, and it does not cover this construction
RM18-boundary	cells at a finite-budget boundary: root_n_and_efficiency/n_500 of canonical-multi-arm-ctmle-selector; double_robust_contraction/treatment_correct_n1500 of canonical-drtmle; double_robust_contraction/outcome_correct_n4000, interval_calibration/correctly_specified and root_n_and_efficiency/n_500 of canonical-multi-arm-drtmle; double_robustness/static__both_wrong and the paired ey_regimen[always] and ey_regimen[treat then continue if l2 positive] rows of weighted-ltmle-crossfit	reading resolved: truth satisfies the gate for the six cells, and comparator SE convention for the two paired rows (tests/diagnostics/rm18_boundary/). Before a future regeneration of weighted-ltmle-crossfit, declare whether it adopts the lmtp standard-error convention for the two paired rows
RM18-one-sided-bias	double_robustness/outcome_correct and double_robustness/treatment_correct of canonical-drtmle, and double_robustness/treatment_correct of canonical-multi-arm-drtmle	reading shared and mixed on the binary rows, and finite-sample excess detected on the multi-arm row (tests/diagnostics/rm18_one_sided_bias/). A declared localization design on 2,000 fresh draws read no increment at the declared resolution (tests/diagnostics/rm19_one_sided_increment/). No validated R comparator fits the multi-arm configuration, so the multi-arm excess has no attribution
RM18-ordinary-weighted	interval_calibration/static__correctly_specified, type_i_error/static__sharp_null and the four targeting_necessity cells of weighted-ltmle	reading finite-sample, contracting, resolved within gate, control underpowered by design and family resolved (tests/diagnostics/rm18_ordinary_weighted/). The static untargeted control discriminates with a probability near 0.72 at the registered 1,200 replicates. Re-declare that control’s law before any regeneration of the study, as the control precedent at 69de6f8 allows
RM18-comparator-density	the paired ate_policy[+0.25 vs natural course] row of shift-policies	reading cleverly density representation (tests/diagnostics/rm18_comparator_density/). The calibration leg fails with a 99% upper endpoint of 0.064762 against a margin of 0.05, so the conclusion is inconclusive. The modified-treatment-policy work kept the density representation. The design ran again after the estimand rename, which draws a new bootstrap stream, and the reading stands
strata-boundary-mean	the two primary truth rows of ey[1][V=2] and the interval_calibration/v2_ey1__correctly_specified, simultaneous_coverage/strata__simultaneous_band and simultaneous_coverage/crossfit_strata__simultaneous_band cells of canonical-stratified-tmle	reading finite-sample Wald interval: the treated mean of stratum V = 2 is 0.9358, and at n = 2,000 the stratum holds about 157 treated rows and about 9 expected non-events. R tmle3 shows the same coverage on the same draws, the bias is inside its margin, and the oracle band at the exact critical value also under-covers (tests/unit/test_band_shortfall_reading.py). The owner closes when a re-declared cell, with its law or size declared before its run, or a small-sample interval correction with its own registered study passes. Until then each cell stays published red under reporting
band-finite-sample	the simultaneous_coverage/all_reported__simultaneous_band cell of canonical-ltmle-survival, the categorical_ltmle__simultaneous_band, categorical_ltmle_crossfit__simultaneous_band and cde_z0__simultaneous_band cells of default-simultaneous-bands, and the clustered_regimens__simultaneous_band cell of clustered-cross-fitted-ltmle, and the six_regimens__simultaneous_band cell of longitudinal-sdr	reading finite-sample, pointwise shortfall inherited: the oracle band at the design critical value also covers below 0.95, and the source study’s pointwise calibration of the same parameters sits near the lower edge of its band. The package critical value averages a little below the design one, so the multiplier explains a small part of each shortfall (tests/unit/test_band_shortfall_reading.py). The owner closes when a re-declared cell, with its law or size declared before its run, or a small-sample interval correction with its own registered study passes. Until then each cell stays published red under reporting
F4-calibration-draws	the interval_calibration/ate__correctly_specified and simultaneous_coverage/arms__simultaneous_band cells of multi-arm-mar-drtmle, which read one set of 2,400 fits	reading finite-sample, one draw set. The SE-ratio interval ends at 0.9294 against a floor of 0.93, and the joint-coverage interval at 0.9196 against 0.92. The calibration fits have an empirical SD 1.037 times their mean standard error. The same configuration gives 0.997 at n_2000 and 0.989 at l3_ate_low__both_correct, on independent draws. simultaneous=True changes no estimate and no standard error. The band critical value averages 2.500 against the oracle 2.508, and the oracle band covers 0.9342 against the package’s 0.9337, so the band construction explains none of the shortfall (tests/unit/test_band_shortfall_reading.py). Pooled over the 4,400 independent both-correct fits of ate[low vs high] at n = 2,000, the spread is 1.020 times the mean standard error (bootstrap 99% interval 0.991 to 1.047), and a Bartlett test across the three cells gives p = 0.20, so the draw set differs from its siblings by no more than chance. No defect was found in the K-arm code. The owner closes when a re-declared cell, with its law or size declared before its run, or a small-sample interval correction with its own registered study passes. Until then both cells stay published red under reporting
composite-high-arm	the ey[high] truth rows of cleverly-composite-drtmle and drtmle-r-composite on the three-arm scenario of composite-missing-drtmle	reading finite-sample, shared with the comparator (tests/unit/test_composite_high_arm_reading.py). Coverage is 0.9225 in the package and 0.9237 in R drtmle, and the 99% intervals end at 0.8949 and 0.8963 against a floor of 0.90. The paired mean difference is 4e-6. The mean standard error is 0.0342 in both, against an efficiency-bound SD of 0.0344 at n = 2,000, so the variance estimate is not low. The empirical SD of the estimates is 0.0367, 1.066 times the bound. The 47 package fits that reached max_outer cover at 0.957, against 0.921 for the fits that met the tolerance, so the cap is not the cause. high has the smallest composite mechanism of the law, 0.070 where W = 0, which holds half the mass. Every other arm and contrast of the scenario passes. The owner closes when a re-declared cell, with its law or size declared before its run, passes, or when a small-sample interval correction with its own registered study does. Until then both rows stay published red under reporting
X4-finite-sample	the sequential_double_robustness/both_correct__n_2000 cell of longitudinal-sdr	reading finite-sample, shared with LTMLE. Coverage is 0.911, with a 99% interval of 0.885 to 0.933 against a floor of 0.90. The bias interval is inside its margin, and the SE ratio is 0.946. The law’s smallest path probability is near 0.012, so an inverse weight can reach about 85. A diagnostic refitted the cell’s fit and the shipped LTMLE with the same learners on 1,000 fresh draws (tests/diagnostics/x4_both_correct/). Both cover 0.903, with SE ratios 0.918 and 0.917. Each standard error correlates with its own error, at 0.301 and 0.321. The same cell at n = 8,000 covers 0.950 with an SE ratio of 0.999 (tests/unit/test_sdr_shortfall_reading.py). The owner closes when a re-declared cell, with its law or size declared before its run, or a small-sample interval correction with its own registered study passes. Until then the cell stays published red under reporting
X8-logit-small-stratum	the interval_calibration/logit_v1_a__correctly_specified and interval_calibration/logit_v2_a__correctly_specified cells of canonical-stratified-incremental-msm	reading finite-sample, inherited from the unstratified fit for stratum 2. The SE ratios are 0.967 and 0.862, and the lower ends of their intervals are 0.927 and 0.782 against a floor of 0.93. Coverage is 0.943 and 0.944. Stratum 1 holds about 600 of the 2,000 rows, and stratum 2 about 400. A declared diagnostic read stratum 2 only. It fitted the shipped unstratified logit MSM on samples of that size from the law given \(V = 2\). That fit under-reports as well, 0.896 against the stratified fit’s 0.867 on fresh draws, and both are calibrated at four times the size, 0.997 and 1.006 (tests/diagnostics/x8_logit_small_stratum/). No diagnostic reads stratum 1, whose interval misses the floor by 0.003. The stratified fit equals the subset fit exactly under fixed nuisances (tests/unit/test_stratified_msm_exact.py), so no defect of the stratified construction was found. The owner closes when a re-declared cell, with its law or size declared before its run, or a small-sample interval correction with its own registered study passes. Until then both cells stay published red under reporting
X8-identity-small-stratum	the interval_calibration/identity_v2_a__correctly_specified cell and the paired msm[W][V=2] row of canonical-stratified-msm-identity	reading finite-sample, smallest stratum. Stratum 2 holds about 400 of the 2,000 rows. The calibration cell’s SE-ratio interval is 0.926 to 1.004 against a floor of 0.93, and on the primary draws the same coefficient reads 0.983 in cleverly and 0.985 in R tmle3. The paired row is inconclusive on its calibration leg alone: the upper limit is 0.0523 against a margin of 0.05, at a resolution of 0.0476. The two estimates differ by 6e-6 on average with the same spread, and R reports a standard error 2.2% above its own spread, consistent with the declared nuisance difference: R fits a Gaussian Lrnr_glm inside each subset (tests/unit/test_band_shortfall_reading.py). No defect was found. The owner closes when a re-declared cell, with its law or size declared before its run, passes. Until then both stay published red under reporting
X8-drtmle-one-sided-bias	the four double_robustness/*__treatment_correct cells of canonical-stratified-drtmle: the marginal ATE and each stratum ATE	reading shared in strata 0 and 1 and mixed in stratum 2, in the vocabulary of RM18-one-sided-bias (tests/diagnostics/x8_drtmle_treatment_correct/). The refit reproduces the committed estimates exactly. On each stratum’s rows, the shipped unstratified DRTMLE and R drtmle 1.1.2, handed the same initial arrays, carry a positive bias too. In stratum 2 the package’s bias, 0.0237, exceeds R’s, 0.0157: the paired difference is 0.0080 with a standard error of 0.0018. The unstratified fit on the stratum’s rows matches the package there to 2e-5, so the excess belongs to DRTMLE at about 400 rows and not to the strata. In stratum 1 the stratified and subset fits differ by 0.0057 (standard error 0.0013). The stratified marginal is the mixture of the stratum estimates, so it inherits their bias: 0.56 of its spread at n = 2,000 (99% interval 0.43 to 0.69) and 0.43 at n = 8,000 (0.25 to 0.61). The intervals overlap, so contraction faster than the spread is not established. No defect of the stratified construction was found. The owner closes when a re-declared cell, with its law or size declared before its run, passes, or when RM18-one-sided-bias closes with a correction that also covers the stratified fit. Until then the four cells stay published red under reporting
X8-drtmle-small-stratum	the two primary truth rows of ey[1][V=2] and the interval_calibration/v2_ate__correctly_specified cell of canonical-stratified-drtmle	reading finite-sample, shared with the comparator. Stratum 2 holds about 400 of the 2,000 rows. Coverage of ey[1][V=2] is 0.900 in the package and 0.8925 in R drtmle on the same draws, with estimates 4e-5 apart on average. The calibration cell’s SE-ratio interval ends at 0.9294 against a floor of 0.93, and on the primary draws the same ATE reads 0.985 in the package and 0.973 in R (tests/unit/test_band_shortfall_reading.py). The owner closes when a re-declared cell, with its law or size declared before its run, passes. Until then the three stay published red under reporting
X16-plugin-variance	the binary_lasso truth row of canonical-ctmle-sequences	reading plug-in variance under near-positivity, shared with TMLE. Coverage is 0.92375, with a 99% interval of 0.896 to 0.946 against a floor of 0.90, and the SE ratio is 0.905. The declaration expected the red: the plan’s probe read 0.899 and 0.881. The final step reports the penalty 0 on 771 of 800 fits, so the reported mechanism is the unpenalized logistic fit. Plain TMLE with the same learners and bounds on the same 800 samples covers 0.9225 with an SE ratio of 0.913. Both cover below 0.85 in the lowest quartile of the reported standard error. On average 10.6% of the true propensity lies outside the bounds of 0.025 and 0.975 (tests/diagnostics/x16_lasso_coverage/, tests/unit/test_x16_lasso_coverage_reading.py). The selection is not the cause, and the row does not test \(\Delta(P_1)\) of F18. The package refuses ci, pvalue and std_error on a lasso fit, which stays correct. The owner closes when a re-declared cell, with its law or size declared before its run, or a small-sample interval correction with its own registered study passes. Until then the row stays published red under reporting
F1-power-design	the power/mix__alternative cell of stochastic-categorical-ltmle	reading underpowered at its declared size. Its n = 4,000 was copied from canonical-categorical-ltmle, where the contrast is 0.125. Here the contrast is -0.0488, so the exact power of a two-sided 5% test is 0.5365, and exact power 0.80 needs n = 7,460. The cell rejects at 0.5575 (99% interval 0.511 to 0.603) against a floor of 0.80, and that interval contains the exact power (tests/unit/test_stochastic_categorical_ltmle_design.py). Its bias is inside the margin and its coverage is 0.9475. The type_i_error cell, on the null variant of the law, passes. The owner closes when a re-declared power cell, with its law or size declared before its run, passes. Until then the cell stays published red under reporting
mtp-longitudinal-limits	the interval_calibration/categorical_mtp__correctly_specified cell of longitudinal-mtp	reading finite-sample, sparse cells: the efficiency ratios read 1.120 and 1.098 against a band of 0.9 to 1.1, and coverage 0.9435 and the SE ratio pass. The cell fits saturated cell probabilities for the six-level mechanism. A diagnostic refitted it on fresh draws. The in-sample fit reads a reported efficiency ratio of 1.103 at n = 2,000 and 1.023 at n = 8,000, and the five-fold fit 1.389 and 1.048, on 300 fresh draws per size. The reported ratio’s excess falls about four times as n grows four times, the order of the cost of estimating sparse cell probabilities, and reads 1.003 at n = 128,000. A wrong bound or an inefficient curve would keep its excess. Both outcome regressions are misspecified, and the saturated mechanism makes the fit the NPMLE whatever the outcome learner, so the estimate is unaffected (tests/diagnostics/longitudinal_mtp_categorical_efficiency/, tests/unit/test_longitudinal_mtp_reading.py). The cell read the same in runs 2 and 3. The owner closes when a re-declared cell, with its size declared before its run, passes. Until then the cell stays published red under reporting
mtp-point-calibration	the interval_calibration/halve__correctly_specified cell of policy-point-mtp	reading Monte Carlo excursion. The SE ratio is 1.0429, with a 99% interval of 1.0011 to 1.0881 against an upper bound of 1.07. It was 1.0430 at 160 bins, so the bin count does not move it. Coverage is 0.9605, and the reported standard error matches the efficiency bound (ratio 1.0018). The influence curve with the binned ratio predicts a ratio of 0.9998. A diagnostic refitted the same configuration on 2,000 fresh draws and read 0.999, with a bootstrap 99% interval of 0.959 to 1.043. Fewer than 1% of its bootstrap ratios reach 1.0429 (tests/diagnostics/mtp_point_halve_excursion/). The diagnostic cannot change the verdict. The owner closes when a re-declared calibration cell for this policy passes, with a budget of no more than 2,000 replications fixed before its run. Until then the cell stays published red under reporting
X19-competing-calibration	the interval_calibration/competing_contrast_x2_h3__correctly_specified cell of longitudinal-incremental-dropout	reading finite-sample, conservative. At n = 96,000 and 3,000 replications the SE ratio is 1.047, with an interval of 1.012 to 1.083 against an upper bound of 1.07. Coverage is 0.959. The reported standard error matches the exact efficient influence-function standard deviation (ratio 1.0006), and the empirical spread sits 4.4% below it. The design probes on other draws read 0.948 at n = 32,000 and 0.980 at n = 64,000 (tests/diagnostics/x19_sizing/reading.csv). The owner closes when a re-declared competing-risk calibration cell passes its band at a budget fixed before its run. Until then the cell stays published red under reporting
X13-finite-sample	the interval_calibration/weighted_t5__correctly_specified cell of point-treatment-survival and the interval_calibration/three_arm_t3__correctly_specified cell of point-treatment-survival-crossfit	reading finite-sample. The weighted cell’s SE ratio is 1.027, with a 99% interval of 0.981 to 1.076 against an upper bound of 1.07. Its reported standard error equals the weighted efficiency bound (ratio 1.0007), and the interval of its empirical efficiency ratio, 0.930 to 1.020, contains one. A diagnostic on 1,000 fresh draws (tests/diagnostics/x13_weighted_calibration/) reads an SE ratio of 1.022 and a coverage of 0.957. The cross-fitted three-arm cell’s empirical efficiency interval is 1.010 to 1.108 against 1.10, with an SE ratio of 1.008. A diagnostic on fresh draws (tests/diagnostics/x13_crossfit_three_arm/) put its reported standard error over the bound at 1.0003 in sample, 1.082 at five folds and 1.055 at ten folds at n = 2,000, and 1.0085 at five folds at n = 8,000, so the excess is the finite-sample cost of cross-fitting saturated cell means. The owner closes when a cell is re-declared with its size and replication count chosen before its run by a stated sizing rule, such as a pass probability of at least 0.90 under exact calibration, and that cell passes. A larger run that happens to pass does not close it. Until then each cell stays published red under reporting
X45-finite-sample	the interval_calibration/nice_g1_treat_all__correctly_specified cell of parametric-gformula	reading finite-sample under the reading that tests/studies/canonical_parametric_gformula.py declares before the run. The cell (n = 2,000, R = 2,400) has an SE ratio of 0.9619, with a 99% interval of 0.9259 to 1.0000 against a lower bound of 0.93. Its coverage is 0.9413, with a 99% interval of 0.9278 to 0.9529 inside the band 0.92 to 0.98. Its bias is 0.000158 with a standard error of 0.000393. The same law, plan and size in two independent draws give SE ratios of 1.0022 (shared_target, R = 1,192) and 0.9701 (ice_reported, R = 1,198). The other G1 calibration cells read 0.972 to 0.993, and the G1 contrast ladder reads 1.021, 0.986 and 1.006 at n = 2,000, 4,000 and 8,000. The study declares an expected 1.26 finite-sample reds over 114 gated cells, and a chance of 0.72 of at least one. The owner closes when a cell is re-declared with its size chosen before its run and that cell passes. Until then the cell stays published red under reporting
F28	X54 parts (d), (f) and (g), for the finite-sample limits of clustered intervals: the fold-evaluated covariate pair of clustered-unequal-cvtmle, and the fold-evaluated bias cells and cross-fitted DRTMLE IID controls of clustered-few-cluster-tmle	each group closes on its own registered study that passes. The fold-evaluated pair of clustered-unequal-cvtmle at 40 clusters in 10 folds: a fold-evaluated degrees-of-freedom rule \(t(\min(J-2, J-V))\) at 40 clusters or more. The three tmle_cv_evaluation__unequal_informative cells: a cluster-size-weighted fold average or another fold-evaluated point whose bias stays inside the margin. The stacked report is the remedy today. The four drtmle_crossfit iid_t_control cells: a calibrated cross-fitted DRTMLE cluster variance, or an IID control that compares the two SEs and not the IID SE with the empirical SD (X54)
mtp-pricing-calibration	the ey_regimen[price_down] and ate_regimen[price_down vs natural_prices] truth rows of pricing_ltmle_tau5 and pricing_sdr_tau5 in mtp-pricing	reading finite-sample, influence-curve variance. At n = 5,000 the coverage is 0.9160 to 0.9230 and the SE ratio is 0.9310 to 0.9518. The standardized bias is at most 0.0342, so the point estimate is not the cause. Each fit reads the exact ratio on the classifier route. The first run at n = 2,000 read coverage 0.903 to 0.912 and an SE ratio near 0.93. A probe on fresh draws read an SE ratio of 0.887 at n = 2,000 and 0.968 at n = 4,000 (tests/studies/canonical_mtp_pricing.py declares the move to n = 5,000). The price_up rows at five nodes pass. The owner closes when a re-declared five-node price_down cell passes, with its size fixed before its run. Until then the four cells stay published red under reporting, and the support rows G39.ltmle.tau5 and G39.sdr.tau5 label the fits experimental
mtp-pricing-learned-density	the three interval_calibration/up_learned_density_tau{2,3,5}__correctly_specified cells of mtp-pricing	reading finite-sample, conservative. The declared 320-bin density gives an SE ratio of 1.0265 to 1.1162 at tau 2, 1.0493 to 1.1408 at tau 3 and 1.0428 to 1.1323 at tau 5. The coverage is 0.9473 to 0.9747. The study declared the three cells reporting before the run, after a screen of 2,000 draws per arm read 1.052, 1.105 and 1.079. The interval errs on the safe side. The owner closes when a re-declared learned-density cell passes its band, with its size fixed before its run. Until then the cells stay published red under reporting
X40-sdr-heavy-ratios	the interval_calibration/p4_sdr__correctly_specified cell of mtp-boundaries, declared reporting before the run	reading finite-sample, influence-curve variance. At n = 4,000 its SE ratio is 0.9408, with a 99% interval of 0.9060 to 0.9775, and its coverage is 0.9357. The LTMLE cell of the same plan reads an SE ratio of 0.9572. The pseudo-outcome learner projects onto [0, 1]. The package labels the SDR interval experimental with these numbers, as it does the five-node price_down rows of mtp-pricing. The cell stays published red under reporting. The owner closes when a re-declared cell passes its band
X20-bootstrap	the interval_calibration cells boot_ey_crossfit__correctly_specified, boot_ate_crossfit__correctly_specified and boot_ate_clustered__correctly_specified of full-refit-bootstrap-and-derived-contrasts	the declared rule 3 keeps the end_of_study/cross_fit and end_of_study/cluster kinds without a support row that lists the bootstrap kind, so their percentile interval carries the label experimental. A diagnostic reading, not a registered result: on this cell the cross-fitted estimator is heavy-tailed. Its 4,000 committed estimates have excess kurtosis 6.7, and about 5% of them lie at the probability boundary, because g_bounds=(1e-8, 1) with saturated cell means leaves sparse training cells unbounded. A bootstrap resample holds about 63% unique units, so more replicates reach the boundary and the replicate spread exceeds the sampling spread (SE ratios 1.23 and 1.27). A probe that kept each unit’s copies in one fold raised the SE ratio to about 1.65, so the split of copies across folds is not the cause. The cluster contrast covers 0.924 with a calibrated SE ratio (0.977), a finite-sample shortfall of the percentile interval at 60 clusters. The owner closes when a re-declared cell for the kind, with its law, size, nuisance bounds or resampling scheme declared before its run, passes a registered cell
X41-negative-control	the three misspecification_control/*_x_contrast__main_terms cells of sequential-baselines (Hajek, Horvitz-Thompson and ICE)	none. The study declares the cells red before the run (EXPECTED_RED in tests/studies/canonical_sequential_baselines.py). A law whose nuisances are all wrong must fail the calibration rule, and tests/unit/test_sequential_baselines_design.py computes the power of that failure. The cells read a standardized bias of 1.7 to 2.0 and a coverage of 0.48 to 0.61, with an SE ratio near 1. A pass would mean the rule cannot detect a misspecified fit

Detailed implementation contracts

The sections below give one contract for each open item. Their physical order does not override the main grid.

RM42. Experimental status and support rows

The Eligibility rule classifies each analysis as supported, experimental, or unavailable. The package labels each estimate supported or experimental, with no opt-in. Each refusal carries a reason code, and How to read a refusal defines the five codes. This row implements the label and the support rows.

part	what it delivers
(a) the experimental label	a label with no opt-in, for a configuration whose target is justified but whose algorithm or inference extension has unresolved evidence. A shown status in cleverly._inference_status and a configuration that no support row covers both give it. Each estimate, bootstrap interval and band carries the label and its reason, and an interval with no computable plug-in curve is withheld
(c) configuration support rows	a support row for each combination of target, estimator, outcome, weighting, splitting, and inference, whose status matches the output
(d) persistence	the experimental status, its configuration key, the support row, and the inference assumptions survive result.save() and cleverly.load()

Each inherited refusal keeps its intervention-specific support checks, the estimator-specific requirements for policy followers, the invalid-event checks, and the identification declarations. A test can detect an observed support failure and check a declared support restriction. It cannot establish population positivity or the absence of unmeasured confounding. A new refusal does not call a stochastic or continuous policy an inappropriate question.

Acceptance:

• a test that an experimental fit carries its label through the summary, the tables, and a save-and-load round trip, and withholds an interval that has no computable plug-in curve;

• a test that each support row matches the status that the fit reports.

X39. Longitudinal evidence over three to five decisions

Every registered end-of-study longitudinal study uses two treatment nodes. The ordinary and cross-fitted categorical studies use complete outcomes, and the known-policy study uses one two-node, three-level law. This row adds laws with three to five decisions, with censoring and realistic support loss, for LTMLE and SDR.

The studies reproduce the existing binary and categorical targets, exercise a nonzero targeting update, and include leakage and covariance controls for the paired policy contrasts. Each page states the conditions for consistency apart from the conditions for valid intervals.

Use R ltmle for the overlapping ordinary regimen and MSM cases, and lmtp for the SDR cases. The cross-fit studies pin lmtp at f04a2b4, which fits the fluctuation on training rows. Upstream 9996b04 fits it on validation rows. Neither runs the pooled update, so label the cross-fitted LTMLE comparison as a different estimator of a shared target. Audit 9996b04 as a second comparator option.

Acceptance: a registered study for each estimator, with the controls above and a pre-queue design review.

Status. The code ships as experimental. It adds the opt-in refit bootstrap for LTMLE and SDR (n_bootstrap, bootstrap_interval="bca", and the studentized bootstrap sup-t band with simultaneous=True), result.diagnostics.influence() and SparseInfluenceWarning. Every new support kind (bootstrap_bca, bootstrap_band) has no support row, so each prints experimental.

The long-horizon Python studies over three to five decisions are pending, as a follow-up pull request. That request is to run the declared studies, move the support rows into the package, and close this row. No coverage result for the new options exists in this repository. The R comparators named above are deferred to X59, so the studies carry Python property evidence only. Do not remove this row until the studies land.

X46. Repeated cross-fitting for longitudinal fits

Point-treatment fits repeat the fold draw and report the median over draws, with the split-adjusted median variance of Chernozhukov et al. (2018), Definition 3.3 and equation (3.14). The repeated cross-fitting study validates that report. Longitudinal fits take n_folds only. This row extends trajectory-level split provenance to repeated fold draws for LTMLE and SDR, and applies the same fixed-repeat rule.

The median does not inherit an ordinary influence function. The contract states the fixed-repeat rule that carries the variance, and it keeps the joint covariance of paired policy contrasts within each draw.

Acceptance: a witness that each draw reproduces a single-draw fit, a mutation control that reuses one draw, and a registered study of the median and its variance.

X33. Longitudinal fitting options

These options belong to the longitudinal fit. They compose with the shipped targeting options of TMLE: iterate=, stopping= and step_bound=, described under stopping rules, step bound and best iterate. Each comparator ships the option, and none needs new theory. Each option keeps every default fit bit-identical, and each changes a fit when it binds.

part	option	what it does	comparator
(d) ratio trim	trim the per-node density ratio at one pooled quantile q of all n x T entries, zeros included, then form the cumulative product	the trimming rule of lmtp: it trims the per-node ratio matrix and not the cumulative ratio. The fit records the trimmed share, as it records truncation now, and takes trimmed_ratio_plugin when the share is above zero. SDR reads the same per-node ratio	lmtp .trim
(e) Markov order	restrict each node’s nuisance history to the last k nodes	a restriction on the observed-data model. The identification summary states it, and the estimand does not change. SDR reads the same per-node ratio and regressions	lmtp k
(i) node bounds	bound each node’s regression into a declared interval before the logistic fluctuation	a fit on a declared range of the iterated mean or of the cause-specific hazard of survival_model="hazard"	survtmle bounds
(j) pooled hazards	fit one hazard regression and one censoring regression over every node, with the node as a covariate, in place of one regression per node	a fit with fewer events per node. A pooled fit is a nuisance choice for survival_model="hazard", which today fits one hazard regression per node and cause and one censoring regression per node	survtmle, MOSS and tmle3 tmle_survival

At a continuous modified-treatment-policy node of LTMLE, the ratio that part (d) trims is the node’s density ratio, which the fit stores as RegimenFit.node_ratio.

Part (i) covers survtmle method = "hazard" as well as method = "mean". On a fit with survival_model="hazard", it bounds each node’s cause-specific hazard. Part (j) applies only to a fit with survival_model="hazard".

The hazard walk of survival_model="hazard" steps along its own path in steps of step_size. It does not read the shipped settings iterate=, stopping= and step_bound=, so LTMLE refuses them beside that model. This item lifts the refusal for the bounded hazard walk.

Acceptance: for each part, a test that the default fit is bit-identical to the fit before the option, an exact test on a finite law, a witness on a law where the option binds, and a mutation control that fails when the option is wrong. Parts (d) and (e) also name their assumption in the identification summary, and a test pins that text. Part (d) pins the trimmed_ratio_plugin record. A registered study covers the parts, with its red cells reported. The R fixtures can stay pending and do not block the merge.

X21. Adaptive-propensity IPTW

cleverly has no inverse-probability-weighted estimator. drtmle 1.1.2 ships adaptive_iptw(), which reports an IPTW estimate with a targeted propensity, in two forms: iptw_tmle and iptw_os. Van der Laan (2014), International Journal of Biostatistics 10(1), derives it. With a propensity fitted by a flexible learner and targeted, the IPTW estimator is asymptotically linear, and its curve needs no outcome regression.

Read the derivation for the targeting of the propensity, the reduced regression it needs, and the interval conditions. drtmle also fits it with missing outcomes and several treatment levels. Each of those is a separate composition with its own contract.

Acceptance:

• exact-law witnesses with a nonzero targeting step;

• a mutation control that drops the propensity targeting;

• a registered study against the pinned drtmle that reuses the DR-TMLE laws.

X26. Plug-in omitted-variable limits with a declared parametric mechanism

ci_lower, ci_upper, robustness_value_ci and rva refuse under nu2_estimator="plugin" (_PLUGIN_LIMITS_REFUSAL in src/cleverly/sensitivity/omitted_variable.py). This item opens them for one declared mechanism. The natural-extension verdicts record the review as part (h).

item	contract
base results	Chernozhukov, Cinelli, Newey, Sharma and Syrgkanis (2026), the bound and its Theorem 4 limits. Saul and Hudgens (2020), Journal of Statistical Software 92(2), for stacked estimating equations and the sandwich variance
step	a stacked estimating equation of (i) the mechanism score \(s(\gamma) = X\{A - \mathrm{expit}(X\gamma)\}\), or the multinomial score, (ii) the second-moment equation \(\alpha(O; \gamma)^2 - \nu^2 = 0\), and (iii) the curves of \(\theta\) and \(\sigma^2\) that ship. The curve of the plug-in \(\nu^2\) is \(\alpha^2 - \nu^2 + \partial_\gamma E[\alpha^2] \cdot \{-J_\gamma^{-1} s\}\). The chain rule and the delta method carry it into the bound
objection search	F26 records no curve for an arbitrary learner, and that case stays refused. DoubleML calls the plug-in “non-orthogonal”, which describes the arbitrary-learner case and not the parametric stack
inherited conditions	a correctly specified mechanism model, because otherwise the plug-in estimates \(\nu^2(\gamma^*) \neq \nu^2_0\); smoothness; an invertible Jacobian. g_bounds makes \(\alpha\) differentiable almost everywhere only, so the contract either requires no active clip at the fit or states that the derivative is zero on clipped rows
learner rule	the bound reads the fit’s own \(\hat g\). So the stack is valid only when the fit’s own treatment learner is the declared unpenalized logistic or multinomial model, or a declared known mechanism. A Super Learner whose library contains that model is refused

A fit with treatment_adjustment= different from adjustment fits its mechanism on the declared subset \(W_g\). The first inherited condition then has two parts: the restriction that the treatment mechanism depends on adjustment only through \(W_g\), and a correct parametric model on \(W_g\).

A declared known mechanism is the degenerate case of the stack. The fit reads \(\hat\alpha = \alpha(g_0)\), so \(E_n[\alpha(g_0)^2]\) is a sample mean of a known function with curve \(\alpha^2 - \nu^2\). The ATT and ATC share term follows by the delta method. The hard-stop review moved this case from F26.

Acceptance:

• a mechanism-score interface for an unpenalized LogisticRegression, binary and multinomial;

• an exact-law Jacobian witness, and a mutation control that drops the \(\gamma\) term and fails;

• the four limits open only under the learner rule, with a refusal test for a Super Learner that contains the model;

• a known-mechanism witness: on a finite law with a declared known mechanism, the reported curve of \(\nu^2\) equals \(\alpha(g_0)^2 - \nu^2\) row by row;

• a registered coverage study.

X58. Per-arm outcome-adaptive C-TMLE intervals with a parametric outcome

This item gives the per-arm outcome-adaptive design a corrected interval in a restricted scope. It takes the tractable part of F19: a regular parametric outcome model with a declared treatment-mechanism contract. F19 keeps the flexible outcome learner, the shared design, local uniformity, and the compositions outside this contract. F19 also keeps the committed red cells. Every configuration outside the support predicate below keeps the generated_design_plugin status.

Part (a) shipped. The in-sample fit with ParametricOutcome and ParametricMechanism reports a stacked-equation interval for ey0, ey1, ate, rr and or. The binary rr and or moved into part (a) because ratio() and contrast() inherit the status. The evidence page states the registered study, which is Python property evidence with no comparator. Parametric per-arm intervals states the contract.

Part (c) is implemented. A cross-fitted fit reads the exact V-fold stack, and repeats above 1 reports the median of the draws. Its study ctmle-oat-per-arm-parametric-crossfit is registered, and its evidence page reports the declared run. Every gated cell passes.

Parts (b) and (d) are implemented. A fit admits three or more arms, known fixed observation weights, the targets ey_obs, par and paf, and the simultaneous band, in sample and cross-fitted. Its study ctmle-oat-per-arm-parametric-extensions is registered, and its evidence page reports the declared run. Every gated cell passes.

An admitted fit with the default simultaneous=True builds a band labelled by the support rows. A fit with repeats above 1, at least two estimates and the default simultaneous=True raises CapabilityError. Four or more arms, estimated weights, a weighted in-sample three-arm fit and repeats with weights have no support row, so they report the experimental label. The text below keeps the part (a) scope for reference and states what each part needed.

What is known. The applied revert and the per-arm evidence page give the cells.

finding	evidence	consequence
a comparator exists	R drtmle 1.1.2 at commit 538a3a2, with adapt_g = TRUE, called once per arm on a binary recode	the comparator does not block this item
cleverly agrees with the comparator	each estimate and standard error agrees to 1e-8 in ctmle-oat-per-arm	parity holds for the uncorrected curve
the reported standard error is too small	ratios from 0.76 to 0.92 over the primary estimands at \(n\) = 1,500. The \(n\) ladder reads 0.83, 0.86 and 0.86 at \(n\) = 500, 2,000 and 8,000	parity does not establish calibrated inference, and it cannot override a measured shortfall
the learned design causes the deficit	the paired cells with \(\bar Q_n\) pinned to the truth read 0.997 and 1.009	learning the predictions adds an omitted contribution
a correction has diagnostic support	tests/diagnostics/x17_generated_design/run.py adds \(c^\top \mathrm{IF}_\beta\) and reads ratios of 1.03 and 0.98, at \(n\) = 1,500 and 6,000	a restricted correction is a concrete candidate
no production correction exists	the diagnostic reads the true \(g_0\) and the outcome learner’s coefficient influence function	each oracle quantity needs an estimable or declared replacement

For arm \(a\), \(g_{0,a}(W) = P(A = a \mid W)\) is the full mechanism, and \(G_a(\bar Q_a(W)) = P(A = a \mid \bar Q_a(W))\) is the adaptive mechanism. The diagnosis identifies this candidate curve for a parametric outcome model with coefficients \(\beta\):

\[ D_{\mathrm{corrected},a} = D_{\mathrm{plugin},a} + c_a^\top \mathrm{IF}_\beta, \qquad c_a = E\left[\left(1 - \frac{g_{0,a}(W)}{G_a(\bar Q_a(W))}\right) \frac{\partial \bar Q_a(W)}{\partial \beta}\right]. \]

\(\mathrm{IF}_\beta\) is the influence function of the fitted outcome coefficients. The formula summarizes the diagnosis. It is not the inference contract.

With a parametric adaptive mechanism, the \(\gamma\) and \(\epsilon\) terms also enter, as follows. With a correct outcome model, the \(\gamma\) terms vanish, and the fluctuation term enters with the factor \(\kappa_a\). The factor is 1 when the mechanism model holds for the projection and no bound binds. With a wrong outcome model, every block enters. Part (a) derived the complete first-order expansion of the fitted estimator, with the outcome fit, the adaptive mechanism fit, the targeting step and the final average.

Readiness. This item is a natural extension candidate with an oracle diagnostic. The hard-stop review reads the in-sample parametric stack as a natural extension. Its base is a stacked M-estimator (Saul and Hudgens 2020) with the conditions of Appendix F of Benkeser, Cai and van der Laan, arXiv:1901.05056v1. The stack, not the curve of Theorem 1, supplies the generated-design term. Theorem 1 needs condition (v), and condition (v) fails here.

The steps are an indicator reduction for each arm, a stacked estimating equation, the chain rule for influence functions, the delta method, and a fixed-dimension stack. This item must confirm that every step is in the standard-step table of Eligibility. A step outside that table returns its claim to F19.

First scope, shipped as part (a). Each extension enters through its own acceptance cells.

axis	first implementation
design	strategy="oat", oat_design="per_arm"
data	independent rows, complete outcomes and treatment, no strata=, no weights
treatment	binary
outcome learner	a declared regular parametric model that exposes its score, its derivative and its coefficient influence function
adaptive mechanism	a declared smooth parametric fit. The contract states its assumptions and the behavior of g_bounds
target	the two arm means, the ATE, rr and or, with their joint covariance
fitting	in sample
inference	a corrected pointwise covariance and a Wald interval, inside the declared model and its regularity conditions

part	extension	entry condition
(a)	the first scope above	the acceptance list below
(b)	more than two arms, ey_obs, par and paf by the delta method, rr and or at more than two arms, and the simultaneous band	a map of the changed contributions, and their own witnesses and cells
(c)	cross-fitting with parametric learners, and repeats above 1	an explicit map of the fold-specific coefficient contributions, and a written expansion. Without one, the claim stays in F19
(d)	fixed known weights	the weight-tilted law of the shipped per-arm contract, with its own witness and cell

The ctmle-oat-per-arm revert cells split by study. Part (a) took the in-sample binary primary rows. The cross-fitted cells interval_calibration/binary_active__correctly_specified and the binary generated_design pair belong to part (c), because those cells cross-fit. Part (c) also takes binary_repeats__correctly_specified. The in-sample three-arm primary rows, the cross-fitted three-arm cells, the three-arm generated_design pair, the simultaneous band and binary_weighted__correctly_specified also cross-fit, so they run on the V-fold stack of part (c).

The study of parts (b) and (d) re-measures them. A cell stays with F19 until its study passes.

Routes compared in part (a). Part (a) evaluated each route, then implemented the smallest justified route. It chose the joint estimating equation. The full-mechanism route is dominated and is not built. It is correct only when the outcome model is correct and \(\kappa_a = 1\), and it needs a declared \(g_0\).

route	what it estimates	conditions to state
a full mechanism	\(c_a^\top \mathrm{IF}_\beta\), plus the \(\gamma\) and \(\epsilon\) terms of the parametric adaptive mechanism, with a declared known \(g_0\) or with a correctly specified parametric mechanism whose score enters the stack. CTMLE refuses a declared treatment_probabilities= today (KNOWN_CTMLE_REFUSAL). This route lifts that refusal for the per-arm correction only, with \(g_0\) an input to the curve and not to the design. Part (a) evaluated this route and did not build it, so the refusal stays	the full mechanism is known or consistently estimated
a joint estimating equation, chosen	the sandwich over \(\beta\), the adaptive mechanism \(\gamma\), the fluctuation \(\epsilon\) and \(\psi\), as X52 describes	the outcome model is correct for coverage of \(\psi_0\), or the clipped mechanism limit equals \(g_0\). The sample Jacobian estimates \(c_a\) from the observed treatment without a full mechanism, as the derivation confirms

A consistent full mechanism is an acceptable cost for valid restricted inference. Avoiding that mechanism is a further objective, and F19 keeps it. A correct outcome model alone does not establish calibrated uncertainty. This item claims no superefficiency and no efficiency gain over ordinary TMLE without a separate argument.

Implementation sequence. Part (a) completed steps 1 to 7. Parts (b) to (d) completed step 8.

1. Derive the complete first-order expansion for the fitted estimator and the learner contract.

2. Name each oracle quantity, and specify an estimable or declared replacement.

3. Evaluate the full-mechanism route, with a known or consistently estimated \(g_0\).

4. Evaluate the joint estimating equation when it accounts for every fitted stage.

5. Compare the routes, and choose one.

6. Compute the covariance from the corrected row-wise curves. Keep the cross-arm covariance for the ATE.

7. Implement the support predicate, and restrict the inferential status to the configurations that meet it.

8. Add parts (b) to (d) only after their changed contributions are mapped and tested.

Release gate. A support predicate, per_arm_parametric_support, replaced the global per-arm flag. The predicate reads the outcome learner, the mechanism learner, the design, the fitting, the target and the inference request. It never reads a fitted array. The predicate admits the compositions that the stacked theory covers. A fit that no support row covers reports its interval with the experimental label. Each part adds its support rows with its registered study.

The corrected status, the covariance and the method declaration survive result.save(), cleverly.load(), contrasts and summaries. RM42 part (c) supplies the support rows. plugin_std_error, plugin_interval and the bootstrap spread stay diagnostics. Ordinary TMLE stays the inference alternative under its own assumptions.

Acceptance for each part.

criterion	evidence
a complete correction	a written expansion, or a standard joint-equation argument, that accounts for the outcome fit, the adaptive mechanism fit, the targeting step and the average
no oracle quantity	the released curve uses quantities that a user can estimate or declare known
an independent check	a tractable law verifies the changed contribution, its sign and the resulting covariance
sensitive witnesses	a mutation that removes or reverses the contribution fails the check. A fixed design removes the learned-design contribution where the derivation says so
the user pipeline	the studies fit the declared outcome and mechanism models. No study supplies an unknown true quantity
calibration	a registered repeated-sampling study measures bias, the standard-error ratio, coverage and the sample-size ladder
joint effects	the study validates the arm covariance and the ATE interval together
comparator scope	R parity stays evidence for the unchanged estimator. The corrected uncertainty is checked independently, because it can differ from R. The Python calibration study gates the merge. An R comparison is registered when it arrives, and it does not block the merge
numerical boundaries	probability truncation and an ill-conditioned fit have explicit behavior and evidence
honest output	an unsupported configuration keeps the diagnostic-only interval. A supported fit states its model and inference conditions

Declare the corrected procedure and the study before the final validation draws. Keep the failed results and thresholds of ctmle-oat-per-arm. Do not relabel an old failure as a pass, and do not widen a margin after the outcome is known.

Run a fresh declared study, or a registered regeneration, for the changed procedure. Reuse the evidence for unchanged components, and add checks for each changed term. Cross-fitting alone is not the correction. A full-refit bootstrap needs its own validity argument for this estimator. Neither removes the generated-design contribution, and neither resolves the irregularity.

When the acceptance passes, close the supported part of F19 only. F19 keeps its other claims and its red cells.

X68. Worked examples for the shipped methods

Review every worked example in docs/examples/ against the methods that ship when every row of milestones B0 to B4 and BP has merged. Start this item only then, so that it covers each method that exists then. A method here means one implementation family of the implementation matrix.

task	required content
inventory	a table that maps each implementation family to the example page or section that shows it, or records that no example shows it
update	each notebook runs on the current API. Replace removed and renamed calls, refresh the stored output, and correct each claim that the current code no longer supports
add	an example for each family that the inventory shows without one. The sequential offers and sequential pricing tutorials count as coverage. After the deletion of the health longitudinal tutorial, no example shows a cluster-robust longitudinal variance (cluster= on LongitudinalTreatment)
index	each new page has a row in the examples index, with its evaluation question, its method entry, and the failure mode it shows. The page and its method entry link to each other, as the examples contract in docs/README.md requires

Use the shared program and study design of the examples index when the method can answer a question in that program. Otherwise, use a synthetic law with a known truth. Use compact data and explicit learners. An example shows normal use of a method. It does not assert a statistical guarantee from one sample.

Acceptance: the inventory shows an example for each implementation family, and every notebook executes in the documentation build.

X69. Documentation review for new and changed methods

Update the reader-facing documentation for each method that the rows of milestones B0 to B4 and BP add or change. Then review all of it for quality. Start this item after X68, so that the review includes the new example pages. The scope is README.md and every reader-facing source in docs/. This item is the broad review that step 1 of the documentation procedure otherwise excludes.

check	required result
coverage	each added or changed method has a user-guide path, a technical-reference entry, an evidence row, and its refusals. The merged pull requests of those rows give the list of methods
correctness	each technical claim agrees with the code, a test, a registered artifact, or a cited source. Correct or remove each claim that does not
clarity	each page follows the documentation procedure
succinctness	each sentence adds verifiable information. Remove repetition, generic introductions, restated headings, closing summaries, and adjectives with no evidence

The succinctness check targets the patterns of unreviewed generated text. Remove them, and do not replace them with other words of the same kind. Keep a table where the content is parallel.

Acceptance: a reviewer other than the author reads each changed page against the four checks and records the findings in the pull request. python -m tests.prose has no unjudged finding, and the documentation build passes with warnings as errors.

X2. Replicate-weight designs

Rust and Rao (1996) govern replication variance for complex surveys. Add BRR, jackknife, or another replicate design only after a source audit matches its construction to this package’s weighted-law estimands and inference conventions.

X35. Efficient known-score ATT and ATC

On data that declares its treatment mechanism, the shipped ATT divides by \(g_0\) and reports the treated mean of \(\bar Q^*_1-\bar Q^*_0\). That curve is not the efficient one when the propensity score is known. Hahn (1998) gives a smaller ATT bound for a known score than for an unknown one.

By the remainder algebra of the known treatment mechanism section, the g-weighted plug-in \(P_n\{g_0(\bar Q^*_1-\bar Q^*_0)\}/P_n g_0\) has the smaller curve. The ATC is the mirror image. No pinned comparator implements it. R tmle and the tmle3 Param_ATT both fluctuate \(g\), so their ATT has the unknown-score curve. The item therefore follows the beta.

item	contract
base result	Hahn (1998), Econometrica 66(2):315–331, Theorems 1 and 2. References records that only the abstract was read. Read Theorem 2 first-hand before the row starts
step	the g-weighted plug-in at \(g_n=g_0\), with the remainder algebra of the shipped known-mechanism ATT
estimator choice	an option on the known-mechanism ATT and ATC. The shipped treated-mean form stays the default
comparator	none. The study cells compare with the truth only

Acceptance:

• an exact-law test of the curve of the g-weighted plug-in;

• a variance witness: on a law where the score carries information, the reported standard error is below the standard error of the shipped form;

• truth-only registered study cells.

X5. Natural and interventional mediation effects

cleverly reports controlled direct effects only. Natural and interventional direct and indirect effects are separate estimands, and each carries its own identification assumptions. Díaz, Hejazi, Rudolph and van der Laan (2021) derive the interventional effects and their efficient influence function under an intermediate confounder. R medoutcon implements a cross-fitted one-step estimator and a cross-validated TMLE for them, and it pins by commit. Read the identification, the influence function, the targeting construction, and the interval conditions first-hand. Add each accepted target to the oracle registry and the evidence gates in both directions.

Mediation under an incremental tilt is a further target of this row. Hejazi, Rudolph, van der Laan and Díaz (2023), arXiv:2009.06203v4, Lemma 3 and Theorems 3 and 4, give its identification and efficient estimators.

X6. Continuous-time survival and competing risks

The shipped survival and competing-risk estimators use discrete time nodes. Rytgaard, Gerds and van der Laan (2022) derive the continuous-time construction, which changes the intensity model, the targeting step, and the remainder. The concrete package implements the one-step form of Rytgaard, Eriksson and van der Laan (2023). Its last release is 1.0.5, and CRAN archived it in 2024, so pin it by commit before it becomes a comparator.

That comparator takes a binary baseline treatment under a static or dynamic intervention, which bounds the paired cells a first study can claim. A discrete-time study is not evidence for a continuous-time interval, so the existing longitudinal rows do not transfer. The discrete-time whole-curve targeting has shipped as hazard-based survival targeting, with survival_model="hazard" and targeting="one_step". On a discrete grid, a concrete intervention on the baseline treatment is a held point-treatment design with a plan at node 1. A stochastic intervention is a known stochastic policy at that node.

X70. Hazard targeting beyond a held baseline treatment

LTMLE with survival_model="hazard" supports one categorical baseline treatment held over every node, with baseline covariates only. The hazard and isotonic survival refusals list each design it refuses. Each refusal names survival_model="iterated_mean" with isotonic=True as the working alternative.

part	what to add	published source
(a) a treatment at several nodes	a hazard model and a fluctuation of the treatment mechanism at each decision node	Stitelman, De Gruttola and van der Laan (2012), The International Journal of Biostatistics 8(1)
(b) covariates after baseline	a model and a fluctuation of each later covariate, beside the event and censoring hazards	Stitelman, De Gruttola and van der Laan (2012)
(c) a continuous baseline treatment or a modified treatment policy	the hazards evaluated at the shifted dose, with the treatment density ratio in the clever covariate	Díaz and van der Laan (2012), Biometrics 68(2), for the point-treatment shift
(d) a working model over the hazard curve	MSM coefficients over regimen and horizon cells from the targeted hazards	Rosenblum and van der Laan (2010), The International Journal of Biostatistics 6(2)

Acceptance:

• exact-law witnesses for each new clever covariate, with a mutation control that drops it;

• a registered study for each part, on a law where the per-horizon and the hazard fits differ.

X7. Two-phase and outcome-dependent sampling

A two-phase design measures some variables on a subsample only. An outcome-dependent design samples on the outcome itself. Each design changes the observed-data likelihood, so each needs its own influence-function correction.

Hejazi, van der Laan, Janes, Gilbert and Benkeser (2021) derive the two-phase correction, and R txshift 0.3.8 implements it. Van der Laan (2008) derives case-control weighting under a known prevalence. Fixed observation weights do not replace either correction. The comparator survey rejects txshift as a second opinion on continuous shifts. That verdict does not carry here, because the two-phase correction is a different feature.

X9. Omitted-variable bounds on the other linear functionals

The package refuses the omitted-variable bound on five kinds of fit whose parameter is a linear functional of an outcome regression. Each refusal is correct, and each message says that the bound is well posed and not implemented. Theorem 2 of Chernozhukov, Cinelli, Newey, Sharma and Syrgkanis (2026) gives the bias of such a functional, and Equation (14) in their Section 4 gives the bounds. The omitted-variable bound study checked those locators against the published online appendix and arXiv v6. This project has not read the published main text, so the source read of this item still needs it.

fit	the functional	what the contract must add
regime axis	a regime mean, linear in the regression of \(Y\) on \((A, W)\)	the representer of each regime, from the fit’s clever covariate
shift axis	a shifted-dose mean, linear in the same regression	the representer of each shift, which reads the treatment density
msm axis	an MSM coefficient, linear in the same regression	the representer of each coefficient through the projection
a response mechanism	the mean of the regression of \(\Delta Y\) on \((A, \Delta, W)\)	a representer that carries \(\Delta\), and \(\sigma^2 = E[\Delta (Y - \bar Q)^2]\)
an intermediate variable	a mean at the level \(z\) of the regression of \(Y\) on \((A, Z, W)\)	a representer with the weight \(1\{Z = z\} / P(Z = z \mid A, W)\)

The response and intermediate representers carry a second mechanism. On those fits the strength \(c_D\) measures a joint strength over the treatment mechanism and that second mechanism. Each contract must state that reading, and its benchmark must measure the same joint strength.

Each contract names the representer, the \(\nu^2\) estimator, and its influence curve. The evidence needs an exact finite-support law for each representer. It also needs a nonzero witness for each weight that is zero off its support, as tests/unit/test_omitted_variable_refusals.py has for the intermediate representer. DR-TMLE and C-TMLE fits stay in F5, and longitudinal fits stay in F16. The ipsi axis stays refused, because its functional depends on the treatment mechanism.

X10. Continuous-dose MSM with a second mechanism

refuse_continuous_msm_mechanisms in src/cleverly/msm.py refuses a continuous-dose MSM fit with a missing outcome or an intermediate variable, in sample and cross-fitted. The clever covariate that the package builds divides by the treatment density at the observed dose and at each dose of the integration grid. build_submodel in src/cleverly/estimators/targeting.py builds it. In that construction, a second mechanism must also divide the covariate at each of those doses. The package does not predict either mechanism at a grid dose. _mechanism_designs and _mechanism_columns in src/cleverly/estimators/_nuisance.py predict a mechanism at each arm, or at the observed and shifted doses, and they have no branch for the grid.

The need for the grid doses belongs to that construction, not to the parameter. A weighted fluctuation takes the regression weights \(\Delta / (g \pi)\) at the observed dose and the covariate \(\varphi(a)\). It needs the second mechanism at the observed dose only. It is the candidate design.

This item is unwritten work rather than a hard stop. The parameter is well posed. The table gives the sources that the source audit starts from, and what this project has checked in each.

mechanism or step	source	what this project checked
the MSM parameter	Neugebauer and van der Laan (2007) define it as a projection of the dose-response curve onto a working model	only at second hand. Section 1 of Kennedy, Ma, McHugh and Small (2017), Journal of the Royal Statistical Society Series B 79(4), 1229–1245, cites them for that projection. This project read that section in the author manuscript, PMC5627792
the response weight	Díaz and van der Laan (2017), Section 2.1 and Equation (1), give it for one arm	the source audit of the stacked arm-indexed contract records that locator
the intermediate weight	none. The package’s controlled direct effect cites no published derivation. Its evidence is the R tmle 2.1.1 comparison of the controlled direct-effect study	the source audit must find a derivation, or record this gap in the contract
the coarsening-at-random mapping of a full-data influence function	Kennedy (2020, arXiv:1802.08952) cites Theorem 7.2 of Tsiatis (2006). Baer et al. (arXiv:2306.16571) cite Theorem 8.3 of Tsiatis (2006) and Theorem 1.3 of van der Laan and Robins (2003)	the citing sentences only. This project has not read either book, so each locator is a candidate for the audit

Match the composition to one published result, or show that it meets the Eligibility conditions. If neither holds, move this item to the future investigations grid.

Acceptance needs two exact-law Gateaux witnesses: one with a nonzero response weight, and one with a nonzero intermediate weight. For each weight, a mutation control must drop that weight and fail. The continuous rule of fit_wide_tilt_refusal must then name the MSM fit. The cross-fitted fit stays in F21.

X11. Learned-policy follow-ups

The learned-rule contract estimates one target by one construction. Each part below is a published follow-up outside that contract. For parts (a) to (e) and (h), the refusal of the request cites the part. No request reaches parts (f) and (g). Each part needs its own contract, witnesses and registered study before it ships, as the learned-rule value did.

part	the request that the contract refuses	published source	readiness
(a) the value of one rule fitted on all rows	cross_fit=False, or one fold	van der Laan and Luedtke (2015), Section 6 and Theorem 5, under an empirical process condition	published support; pending source read
(b) learned longitudinal regimens	DynamicRegimen(..., rule_kind="estimated")	van der Laan and Luedtke (2015), Sections 2 and 7, at two time points	published support; pending source read
(c) a contrast of the learned-rule value with a known regime or an arm	learned_rule= beside interventions= or an arm estimand	Theorem 6 of the same paper for each value. The contrast follows by linearity of the fold-local curves, an Eligibility step that the contract must record	source audit
(d) categorical treatments	a treatment with more than two arms	Nordland and Holst (2026), Section 3.4, for discrete actions	source audit
(e) the stacked doubly robust score evaluation	cv_evaluation=False	Nordland and Holst (2026), Algorithm 4, which pools the scores and centres the variance at the pooled estimate	published support; pending source read
(f) the value of the optimal rule	no request reaches it	van der Laan and Luedtke (2015), Section 7.2, last paragraph; Luedtke and van der Laan (2016), Annals of Statistics	published support; pending source read
(g) blip and weighted-classification rule learners	no request reaches it, because the contract has one rule learner	Luedtke and van der Laan (2016), International Journal of Biostatistics, Sections 4.1 to 4.3, read first-hand in the author manuscript	published support
(h) fold-specific targeting	targeting_scheme="fold"	Montoya, van der Laan, Skeem and Petersen (2023), International Journal of Biostatistics 19(1):239–259, Section 3.2, Step 2(c), and Section 4.2, read first-hand in the publisher’s version	published support

A rule learned on separate training data and frozen before evaluation is a known rule. Rule(..., rule_kind="known") and DynamicRegimen(..., rule_kind="known") evaluate it, and the interval targets that rule conditional on the training data. A report that selects the best of several estimated rules changes the meaning of the reported value (F27).

The hard-stop review adds the parts below. Each one holds under condition C3 in its fixed-limit form (van der Laan and Luedtke 2015, Theorem 6), and its refusal cites the part. Part (c) also covers a learned rule beside another parameter axis. Under C3 the fixed-dimension stack carries that case, and it shares the source audit of part (c).

part	the request that the contract refuses	step	readiness
(i) the mean over a fixed number of splits	repeats above 1	linearity over a common limit. Under the fold-average target that the package reports, the median of split estimates estimates no defined parameter, so it stays refused	natural extension
(j) a learned rule with a controlled intermediate	intermediate=	a two-time-point rule pair: the learned rule at \(A\) and the static \(Z = z\)	source audit, with part (b)
(k) observation weights	weights=	the chain rule with a known weight. The contract states whether the rule learner reads the weights	natural extension
(l) clusters	id=	a cluster as the unit, with the few-cluster rules of F28	natural extension
(m) baseline strata	strata=	a finite partition, after X28	natural extension
(n) the omitted-variable bound	the bound on a learned-rule fit	the bound of the frozen fold rules after X9. Its limits need \(\sigma^2\) and \(\nu^2\) asymptotically linear under C3, or the row ships the point bound only	natural extension
(o) simulated confounding and refute	either on a learned-rule fit	a new fold-evaluated replay path with the fold rules frozen. It reads as confounding of the value of these fixed rules	natural extension

Part (h) is not the training-fold update that the Eligibility section names as new theory. Montoya and co-authors fit the update on the validation rows, and the package already ships that update for arm targets.

X28. Fold-evaluated CV-TMLE with baseline strata

cv_evaluation=True refuses strata= before any learner (src/cleverly/estimators/tmle.py). The fold-evaluated estimate needs the stratum shares \(P_n(S=s)\) and a stratum-indexed fold average inside each validation fold. The pooled stratified update is unchanged. The item follows the beta because no pinned comparator reports a fold-averaged stratified estimate. The tmle3 CV-TMLE evaluates a pooled mean over the validation predictions, and the shipped cross_fit=True pooled fit is that estimator.

item	contract
base results	the shipped fold-evaluated estimate (CV-TMLE) and the shipped stratified fluctuation (point-treatment TMLE)
step	a finite partition. Each stratum estimate is the fold average of the stratum plug-ins of the validation folds. Each stratum curve is \(I(S=s) D_s / P_n(S=s)\)
objection search	the natural-extension verdicts, part (i), found no objection to a finite partition in Kennedy (2019), Benkeser et al. (2017), or the MSM projection contract. The fold-evaluated base estimate is Zheng and van der Laan (2011), Sections 2 and 2.1, which F21 cites. No source read records the stratum restriction of that estimate as open
inherited conditions	the conditions of the fold-evaluated estimate inside each stratum; positivity inside each stratum; a fixed number of strata

Acceptance:

• a fold-evaluated stratified fit whose stratum estimates equal the fold average of the per-fold stratum plug-ins;

• an exact-law test of each stratum curve;

• a registered calibration cell.

X32b. Repeated outcomes for SDR and IPSI

LTMLE and IPSI fit a repeated outcome, declared with outcome=Repeated([...]). Each horizon is the end-of-study fit of the panel truncated after it (repeated outcomes). The fit refuses a repeated outcome for any other estimator kind, before any learner. So SDR refuses it now.

part	what to add	evidence
(a) SDR	the per-horizon reduction of the sequentially doubly robust fit	the reduction test of tests/unit/test_repeated_outcome.py for SDR, and exact-law Gateaux witnesses
(b) IPSI	the curve \(t \mapsto E[Y_t^{Q}]\) under a tilt. Kim, Kennedy and Naimi (2021), Journal of Causal Inference 9(1):302–344, Theorems 3.1, 4.1 and 5.1, cover tilts, dropout, and the joint process over \(\delta\) and \(t\)	shipped, with the reduction test and the exact-law witnesses E5 to E8. The registered study longitudinal-repeated-ipsi passes all 96 property rows, 81 gated and 15 reported

Acceptance:

• tests/unit/test_repeated_outcome_subclasses.py passes with each estimator fitting rather than refusing;

• exact-law witnesses with a non-absorbing outcome that returns to zero, and a mutation control that seeds every horizon at \(Y_T\);

• a truth-calibrated registered study per estimator, or a row in longitudinal-repeated-outcome for each. Kim’s research code is unpinned, so IPSI has no paired comparator.

X47. Simulated-confounding laws for point-treatment fits

simulated_confounding refuses seven compositions on a point-treatment fit. The hard-stop review found a declarable law for each part below. Each law is a declaration with a stated reading, not an estimator claim. The base law is the pinned DoWhy refuter, _include_confounders_effect at commit 2116d5c.

part	request	law and reading	witness
(a)	a multi-arm treatment	the binary flip applied to the two arms of a declared pairwise contrast \(a\) against \(b\): \(g'_a = (1-s)g_a + s g_b\). The swap is label-invariant by construction. A \(K \times K\) transition is not adopted, because no source gives its reading	swapping the arm codes gives identical cells
(b)	a clustered fit	the caller declares latent_level as "row", "cluster", or mixed with a declared \(\rho\). "row" is refused when the treatment is constant within clusters. treatSens 3.0 (R/genU_contY.R) is a design precedent for the level, not a base	a cluster-level latent is constant within each cluster
(c)	a categorical benchmark covariate	a block calibration over every encoded column of one logical covariate, fitted unpenalized. The shipped helper’s default L2 penalty breaks reference invariance, so the contract changes the fit	relabelling the reference level gives the same strength
(d)	estimated weights	hold the supplied weights fixed. Each cell targets the fit’s weighted population, \(E[w\,h(W, A', Y')]\). Regenerating the weights is not adopted, because it defines no population that the fit targets	the replay at zero strength reproduces the weighted estimate. At a declared nonzero strength on a finite law, the replay cell equals \(E[w\,h(W, A', Y')]\) computed exactly. A mutation that drops \(w\) from the perturbed refit fails that check
(e)	a missing outcome or a missing treatment	outcome-axis cells, and a declared observation mechanism that reads the covariates only, so \(\Delta \perp (A', Y') \mid W\)	a mutation that lets the mechanism read \(A\) fails the declaration check
(f)	an intermediate	outcome-axis cells, and an intermediate-axis law that flips or shifts \(Z\) in the latent tail and shifts \(Y\) with \(A\) held: \(g_{Z'} = (1-s)g_Z + s(1-g_Z)\)	\(A\) is unchanged. A mutation that flips \(A\) fails
(g)	a declared q_bounds	an outcome shift on the logit scale of \([a, b]\). Values stay inside, and the law is the identity at zero strength. The report gives the share of rows at a bound, which never move. A normal-score option has lower confidence. That option uses \(\hat F = \mathrm{rank}/(n + 1)\), so \(\Phi^{-1}(\hat F)\) stays finite	each perturbed outcome stays in \([a, b]\)

Readiness: natural extension, and no new theory for part (d). No part makes an interval claim. F12 and F15 keep the parts that need identification.

Acceptance: each part’s witness; a pre-fit refusal test for each request that stays refused; the existing refusal constants changed in the same commit.

X48. Longitudinal simulated-confounding replay with a time-fixed latent

One time-fixed latent is shared by every treatment node, and the DoWhy law applies at each node. The contract covers uncensored terminal-outcome fits whose panel has no time-varying covariate after the first treatment node. That narrowing removes covariates that were generated under the original treatment. Censoring, survival outcomes, post-treatment covariates and time-varying latents stay in F13.

A later treatment node has the same structure as a post-treatment covariate when its mechanism reads an earlier treatment. The data generated \(A_2\) under the original \(A_1\), so given the misclassified \(A'_1\) the node \(A_2\) depends on the latent. The induced association of \(A_2\) with the latent then includes the path through the earlier misclassified treatment. The contract must do one of two things before it ships:

option	contract
define the induced association	the reading of each strength names the induced association at a later node, including the path through \(A'_1\), and the replay reports it
restrict the mechanisms	the replay covers only fits whose declared treatment mechanism at each later node does not read an earlier treatment, and it refuses the others before any draw

Until the contract chooses one, a later node whose mechanism reads an earlier treatment stays in F13.

Acceptance: the replay at zero strength reproduces the estimate; a nonzero witness at a two-node law; a pre-fit refusal for each panel outside the contract; for the restricted option, a pre-fit refusal of a mechanism that reads an earlier treatment.

X49. E-value for a controlled direct effect

The target is the package’s controlled-direct-effect risk ratio between arms \(a\) and \(a'\) at a fixed \(Z = z\). The hard-stop review records the verdict.

item	contract
step 1	the bias of the ratio splits into one factor per arm. The split is an identity
step 2	each factor is bounded by the bounding factor of Ding and VanderWeele (2016, Epidemiology), eAppendix Proposition A.2 (arXiv:1507.03984v1). The strengths are suprema over \(w\). Arm \(a\) uses the ratio \(\sup_u P(u \mid a, z, W) / P(u \mid W)\). Arm \(a'\) uses the reciprocal direction \(\sup_u P(u \mid W) / P(u \mid a', z, W)\). Each arm has its own \(RR_{UY \mid \cdot}\)
precedent	Smith, Mathur and VanderWeele (2021), arXiv:2005.02908v1, Result 1, whose \(BF_s\) is a per-arm product
inversion	with equal strengths, the ordinary E-value of \(\sqrt{RR}\). The limit uses the confidence limit nearest the null, as the shipped rr E-value does. The odds-ratio and Gaussian conversions keep their approximation label
reading	the cell ratio \(\sup_u P(u \mid A = a, Z = z, W) / P(u \mid W)\) mixes the association of \(U\) with \(A\) and with \(Z\), and the report names it so
inherited conditions	\(Y_{az} \perp A \mid W, U\) and \(Y_{az} \perp Z \mid A, W, U\), with \(U\) a baseline latent that \(A\) does not affect; positivity given \((W, U)\). The strengths are suprema over \(w\)
context	VanderWeele (2010), Epidemiology 21(4):540-551, Theorem 1, assumes that \(U\) confounds only \(Z\) and \(Y\). It is context, not the base

Acceptance: a nonzero finite law where a single bounding factor fails and the product holds; a wrong-arm control that fails.

X50. Further DR-TMLE compositions

The base is Benkeser, Carone, van der Laan and Gilbert (2017), Theorem 1 (PMC5793673), in sample.

part	request	step
(a)	interventions=	an indicator reduction to \(1\{A = d(W)\}\). A known stochastic policy is a known tilt in \(W\) for each arm
(b)	msm= over discrete arms	a fixed full-rank projection of the arm or regime means
(c)	NaturalCourseMean, PAR and PAF with missing outcomes	Theorem 1 with \(\Delta\) as the treatment and \((A, W)\) as the covariates, then a stack, linearity for PAR and the delta method for PAF
(d)	evaluation= on the composite	a diagnostic only. No new theory
(e)	the omitted-variable bound	the shipped plug-in bound recentred on the DR-TMLE point, under a consistent mechanism. No new theory. The owner chooses the scope
(f)	estimated weights with a guard	the conditional reading of the weights does not use efficiency, so it covers the fixed-weight DR-TMLE curve. It reopens estimated_weight_plugin for DRTMLE

Part (c) has four steps.

step	work
1	a realised-arm composite view in estimators/composite.py, with the indicator \(\Delta\) and the covariates \((A, W)\), and reduced regressions over \(\bar m(A, W)\) and \(\pi(A, W)\)
2	the DR-TMLE natural-course mean ey_obs at each guard and reduction, with Gateaux and remainder witnesses for the corrected curve \(D^*-D^*_Q-D^*_g\), and its post-fit readers
3	PAR and PAF through the shipped TargetContext.natural_course hook
4	a registered study with one-wrong and both-wrong cells, paired with drtmle 1.1.2 through the constant-treatment form (A = rep(1, n), W = cbind(A, W), DeltaY = !is.na(Y)). Its one-wrong cells declare their reading from the case table

Acceptance: a nonzero witness for each changed term; a registered study for each interval claim.

X51. C-TMLE point estimates for further targets

Points only. Every fit keeps working_mechanism_plugin or generated_design_plugin. The observation factors stay full-covariate and off the selection path, as the shipped selector fits them. A path that holds them needs its own derivation and is out of scope.

part	request	step
(a)	the natural course, PAR and PAF with missing outcomes, and cross-fitted arm-indexed missing outcomes, on a selector strategy or the shared design	an ordinary natural-course TMLE stacked beside the C-TMLE arm mean (van der Laan and Gruber 2009, WP 246, Section 2.4)
(b)	interventions=	an indicator reduction to \(1\{A = d(W)\}\) (WP 246, Theorem 2)
(c)	msm= over discrete arms	a fixed full-rank projection of the arm means, with a declared selection criterion
(d)	a missing treatment on a selector strategy, in sample	the composite indicator reduction
(e)	id=	a cluster as the unit with whole-cluster folds. Each point inherits the fixed-limit assumption for the selected mechanism (WP 246, Section 4)
(f)	the omitted-variable bound	as X50 part (e). No new theory

Acceptance: a nonzero witness for each changed term; a registered point study.

X52. Parametric C-TMLE intervals

The base is a stacked estimating equation (Saul and Hudgens 2020) over every parameter of a fully parametric fit: the outcome GLM \(\beta\), the design or candidate mechanism \(\gamma\), the fluctuation \(\epsilon\) and \(\psi\). The sandwich supplies the generated-design term and every other term.

part	request
(a)	a selector fit with one declared partial candidate and parametric learners
(b)	the composite cells of the per-arm outcome-adaptive design (baseline strata, a missing outcome, a missing treatment), with a parametric outcome, in sample. It builds on X58, which holds the plain per-arm cells
(c)	the shared design with a parametric outcome and a parametric multinomial design
(d)	the clustered versions of parts (a) to (c) and of the X58 cells, with the few-cluster rules of F28

item	contract
learners	unpenalized parametric learners, read from the fit’s own learners, as in X26
bounds	g_bounds inactive at the limit
coverage, part (a)	coverage of \(\psi_0\) needs the outcome GLM correct, or the candidate mechanism equal to \(g_0\). Otherwise the interval covers the pseudo-true limit
coverage, parts (b) and (c)	coverage of \(\psi_0\) needs the outcome GLM correct. Otherwise the interval covers the pseudo-true limit
regularity	regular in the declared outcome model. Under a correct candidate mechanism, part (a) is regular in the model where that candidate holds. No part claims regularity over the nonparametric model

Acceptance: separate nonzero laws for the outcome and mechanism terms; a mutation that drops the \(\epsilon\) and \(\gamma\) terms at a law where the design limit differs from the projection; a registered study.

X53. Missing-outcome CV-TMLE variants

part	request	step
(a)	targeting_scheme="fold" with missing outcomes	Montoya et al. (2023), Section 3.2, Step 2(c), with the composite indicator reduction. The coefficient is fit on the validation rows
(b)	repeats above 1 with the median	base: the shipped stacked contract (Zheng and van der Laan 2010, WP 273, Theorem 1, with the composite indicator reduction), for a fixed number of splits. Each draw is \(\psi_0 + P_n D + o_P(n^{-1/2})\) with common nuisance limits, so the median is too. No independence between draws is needed. The split-dispersion term is \(o_P(n^{-1})\), so its benefit is a finite-sample evidence claim
(c)	a cross-fitted TMLE with a missing treatment	a product of fold-local factors estimates \(P(C_a = 1 \mid W)\)
(d)	shift, regime, controlled-direct-effect and MSM targets, cross-fitted with missing outcomes	Díaz, Williams, Hoffman and Schenck (2023), Theorem 3 (arXiv:2006.01366v4), with \((A, \Delta)\) as the exposure. An MSM adds the projection. The incremental and risk-ratio tilt axes are pending a source read of Kennedy (2019) and Kim et al. (2021), because Theorem 2 assumes that the regime does not depend on \(P\)
(e)	the four stacked follow-ups	the fold-evaluated construction, supplied split plans, the bounded-continuous stacked natural-course mean, and stacked targets with baseline strata. Each has its own contract and evidence

F21 keeps the cross-fitted DRTMLE compositions. Acceptance: a nonzero witness for each changed term; a registered study for each part.

X54. Small-sample evidence for clustered intervals and boundary nodes

The cluster-as-unit theory is the same at 4 clusters as at 10. Each part below needs a registered measurement or a declared construction, not a theorem. F28 stays the owner id of the clustered red cells, and this row is the work that closes them.

part	request	the evidence that reopens it
(a)	an interval at 4 to 9 clusters, or at 4 to 19 for in-sample LTMLE	a registered measurement. At 4 clusters a pre-run probe found 0.25% to 9% of draws on which a fit cannot run, because the outcome does not vary among one plan’s followers or a training fold lacks an outcome class
(b)	a cross-fitted LTMLE interval at 4 to 19 clusters	a registered measurement. few-cluster-cross-fitted-ltmle measures 20 and 30 clusters only
(c)	a small-sample reference other than \(t_{J-2}\)	a reference with its registered study. Nugent et al. (2024), Section 2.2, and Benitez et al. (2023), Sections 3.1.2 and 3.2.1, state \(t_{J-2}\) for cluster-randomized trials. Fang et al., arXiv:2510.08438, Section 3.3, gives another
(d)	a fold-evaluated interval at 40 clusters or more	a fold-evaluated degrees-of-freedom rule \(t(\min(J-2, J-V))\) with its own registered study. The unequal-size study’s pair at 40 clusters in 10 folds reads coverage 0.9325, with lower endpoint 0.918 against the 0.92 floor
(e)	the fold-evaluated variance at few clusters per fold	a calibration result for the centered fold cluster variance. The few-cluster study measures it at 2, 4 and 6 clusters per fold
(f)	a fold-evaluated point at informative unequal sizes with few clusters per fold	a construction whose bias at 2 to 6 clusters per fold stays inside 0.25 empirical standard deviations, such as a cluster-size-weighted fold average. The study reads a bias of 0.61, 0.43 and 0.32, where the stacked fit reads 0.14, 0.10 and 0.06 (tests/unit/test_fold_evaluated_ratio_bias.py)
(g)	a calibrated cross-fitted DRTMLE cluster variance at 10 to 30 clusters	a variance whose SE ratio stays inside the calibration band, or a redesigned IID control. The study reads cluster-robust SE ratios of 1.19, 1.14 and 1.12 at 10, 20 and 30 equal clusters
(h)	complex nuisance learners at about 20 clusters	a registered study. Wang, Park, Small and Li (2024), accepted manuscript PMC11795269, Section 4.2, Remark 3, recommend parsimonious working models at about 20 clusters. The registered evidence uses parametric nuisance learners only
(i)	an interval at a boundary node estimate, at a fixed law	a declared node-variance construction and a registered study where zero-event nodes are common. At a law with interior hazards, and a node risk set that grows linearly in \(n\), a zero-event node has exponentially small probability. An interval that differs from the ordinary one only on that event is then valid at every fixed law under the shipped theorem. A law with a true node hazard of exactly 0 or 1 is neither interior nor in the local regime, so the construction must be conservative there, or F31 keeps that case

F31 keeps the rare-event regime, and F28 keeps fits below 4 clusters. Acceptance: each part’s registered study passes under a declaration fixed before its run.

X55. Bootstrap extensions

part	request	base	conditions
(a)	the natural-course, PAR and PAF bootstrap with missing outcomes, in sample	the bootstrap of a smooth M-estimator, Tang and Westling (2024), arXiv:2404.03064v2, Theorem 3.4	finite-dimensional nuisances, read off the fit’s own learners, as in X26; a registered study
(b)	the HAL-TMLE bootstrap	Cai and van der Laan (2020), arXiv:1905.10299, Section 3.6, Theorem 4	in sample; a HAL learner, which does not ship; \(C\) fixed at the selected value; a per-replicate update
(c)	the model-based targeted bootstrap	Coyle (2017), Berkeley dissertation, Section 1.4 and Appendix A.3, Theorem 9 (thesis numbering). The book chapter of Coyle and van der Laan (2018) was not read	resampling from the targeted fit, with Super Learner and TMLE refitted and retargeted on each sample. Theorem 9 needs the efficient score solved to the order it states, a negligible remainder, a uniform Donsker class, and \(L_2\) convergence of \(D^*\). The local read records that order as \(o_P(1/n)\), and the row confirms it against Theorem 9 before it ships. The nuisance rates \(o_P(n^{-1/4})\) under the targeted fit, positivity and bounded sectional variation come from Lemma 2 and Corollary 1, for the treatment-specific mean only. Other targets need their own rate lemma

F2 keeps bootstrap consistency with data-adaptive or cross-fitted nuisances. Acceptance: a registered coverage study for each part.

X56. Competing-event intervention targets

part	target	base	readiness
(a)	the risk under eliminated competing events	Young, Stensrud, Tchetgen Tchetgen and Hernán (2020), arXiv:1806.06136v3, Sections 5, 6.1 (Equation 23) and 8.1. The competing event is a censoring event. The shipped censored LTMLE fits a composite censoring indicator \(1\{C_t = 1, D_t = 0\}\) placed after \(D_t\) in the node order, with \(C_t = 1\) meaning that the unit remains under observation	published support
(b)	separable effects with baseline covariates	Stensrud et al. (2022), arXiv:1901.09472v2, Section 5.2, formula (5), with the estimator of Wang et al. (2025), arXiv:2304.04904v1, under \(Z_t := D_t\)	source audit
(c)	separable effects with time-varying common causes	Stensrud, Hernán, Tchetgen Tchetgen, Robins, Didelez and Young (2021), Lifetime Data Analysis 27(4):588-631, Section 6.2, Equation (19), with the Wang et al. (2025) estimator under \(Z_t := (L_{A_D,t}, D_t)\)	source audit

The source audit of parts (b) and (c) checks the node order, the user-declared partition of \(L_t\), and the efficient influence curve. No data check can verify the dismissible-component conditions. Acceptance: oracle and evidence gates for each target in both directions.

X57. Joint intervention axes and tilt compositions

part	request	step
(a)	two intervention keywords in one fit	separately targeted fits on the same rows, one per axis, then a fixed-dimension stack for the joint curve and covariance. Linearity gives cross-axis contrasts. An incremental axis does not share \(g^*\) with a regime axis
(b)	msm= over declared regimes, shifts or tilts	the shipped MSM score with the arm indicator replaced by \(1\{A = d(W)\}\) (an indicator reduction) or by \(q(a \mid W)\) (a finite categorical sum). A tilt adds its mechanism term for each declared \(\delta\). The score carries the effect modifiers \(V\)
(c)	an arm MSM beside another axis	a fixed-dimension stack
(d)	the MNAR tilt on a shift fit or an incremental fit	the point curve \(E[\bar Q_\gamma(d(A, W), W)]\) on a shift fit, and \(E[\sum_a q_\delta(a \mid W) \bar Q_\gamma(a, W)]\) on an incremental fit. At \(\gamma \neq 0\) the spread columns use the plugin_std_err and plugin_interval_* names, and no interval is claimed
(e)	a controlled direct effect under a tilt	a redirection to the shipped two-node IPSI plan, a tilt node and then a label node \(Z = z\) (part (s) of the natural-extension verdicts). The refusal names the call

Acceptance: each composition reduces exactly to each standalone fit; nonzero controls for every cross-axis block; a registered study for each interval claim.

X59. Long-horizon comparator parity for LTMLE and SDR

The X39 studies over three to five decisions carry property evidence only. No comparator ran. This row adds the comparator readings that X39 deferred.

Use R ltmle 1.3-0 for the ordinary regimen and MSM scenarios of long-horizon-ltmle. Use R lmtp for long-horizon-categorical-ltmle and long-horizon-sdr. The shipped cross-fit studies pin lmtp at f04a2b4, which fits the fluctuation on training rows. Upstream 9996b04 fits it on validation rows. Neither runs the pooled update, so label the cross-fitted LTMLE comparison as a different estimator of a shared target. Complete the 9996b04 audit and choose the pin.

The design needs a K-node ltmle runner, two 9996b04 adapters and an image, parity gates, a chunked sample hand-off, and an R budget. Three points stay open: the source of the parity tolerance, the memory gate, and the order of the two phases.

Acceptance: each X39 study record moves its pending_reference to reference and clears pending_reason, the stub runners give way to the real runners, and each study is regenerated with its reference. The parity gates and the margins rows are declared before the run, after a pre-queue design review.

X60. Settings of the stacked and natural-course contracts

Two audited contracts refuse the requests below. The first is the cross-fitted arm-indexed stacked contract with missing outcomes. The second is the missing-outcome contract of NaturalCourseMean, PAR and PAF. That contract refuses the three targeting settings in sample and cross-fitted. It refuses weights and clusters when it is cross-fitted. Each refusal raises before any learner, in estimators/tmle.py.

part	request	step
(a)	fluctuation="linear", one-step targeting, and target_weights=True, on both contracts	each setting changes the submodel only. The in-sample TMLE ships each setting for arm targets. Estimator options states that each one solves the same score. No new theory is needed
(b)	att and atc on the arm-indexed stacked fit	the shipped in-sample missing-outcome ATT and ATC curves, cross-fitted under Zheng and van der Laan (2011), WP 273, Theorem 2. That theorem leaves an empirical component untargeted, as the references record. For the ATT, that component is the treated share and the covariate law of the treated. The ATT coordinates join the joint fluctuation over the stacked validation rows
(c)	observation weights and clusters on both stacked fits	known weights in each targeting equation, and a cluster as the unit with whole-cluster folds. The clustered fit inherits the four conditions of grouped folds: independent clusters, equal cluster sizes, no interference, and the usual remainder rates. F22 records the same conditions
(d)	intermediate= beside a natural-course target	the mean \(E[\bar Q(A, z, W)]\), which sets \(Z = z\) and leaves \(A\) natural. It is an indicator reduction to \(1\{Z = z\}\) with \((A, W)\) as the covariates, as X50 part (c) uses for \(\Delta\). It holds under the controlled-direct-effect conditions \(Y(a, z) \perp Z \mid A, W\) and \(P(Z = z \mid A, W) > 0\). The contract states both. With missing outcomes the indicator is \(\Delta \cdot 1\{Z = z\}\). PAR follows by linearity, and PAF by the delta method

The curve of part (d) is \(1\{Z = z\}/P(Z = z \mid A, W)\,(Y - \bar Q(A, z, W)) + \bar Q(A, z, W) - \psi\). A reading of the natural course as the observed \(E[Y]\) sets no intervention. That request is different_estimand, not a gap.

Acceptance needs each check below.

• unit weights reproduce the unweighted stacked fit exactly;

• one-row clusters with the same folds reproduce the iid stacked point and curve;

• part (d) at a law where every unit has \(Z = z\) equals the shipped natural-course mean;

• each setting of part (a) solves the stacked score to solver tolerance at a finite law;

• a nonzero witness for each changed term;

• a pre-fit refusal test for each request that stays refused;

• a registered study for each interval claim.

X61. Fold targeting and fold evaluation

The fold-specific update fits the fluctuation on the validation rows. Montoya, van der Laan, Skeem and Petersen (2023), Section 3.2, Step 2(c), publish that update, as X11 part (h) records. Zheng and van der Laan (2011), WP 273, choose one pooled fluctuation. The references record that WP 273 does not validate a separate fluctuation in each fold. The parts below compose the fold-specific update, or the fold-evaluated report, with settings that the package refuses.

part	request	step
(a)	targeting_scheme="fold" with incremental=	each fold’s update solves the efficient influence function equation of Kennedy (2019), arXiv v3, Theorem 2, on its validation rows. That equation includes the mechanism term. The fold average is the estimator of Section 4.2, Algorithm 1, and Section 4.3, Theorem 3, gives its limit
(b)	baseline strata with targeting_scheme="fold"	a finite partition of the fold-specific update. Each stratum solves its own fold-specific equation, and the strata are stacked
(c)	cv_evaluation=True with rr, or or msm=	the delta method on the fold-evaluated arm means for a ratio, and a fixed full-rank projection of those means for an MSM. The estimator is the ratio of the fold averages, not the fold average of the fold ratios

F18 keeps a fold-specific selection on the C-TMLE selector paths. F19 keeps the fold average of strategy="oat". F5 keeps DRTMLE with fold targeting or fold evaluation. F32 keeps outer folds stratified on the treatment or the outcome.

Acceptance needs each check below.

• one stratum reproduces the unstratified fold-specific fit exactly;

• the fold-evaluated ratio equals the ratio of the reported fold-evaluated arm means exactly;

• a nonzero witness for the mechanism term of part (a);

• a pre-fit refusal test for each request that stays refused;

• a registered study for each interval claim.

X62. Other DR-TMLE and C-TMLE compositions

F5 keeps the compositions that need a new regularity or asymptotic argument. F21 keeps reduced_crossfit="nested" on the randomized missing-outcome DRTMLE. X50 and X51 hold the compositions that moved. This item holds the other refused compositions of DRTMLE and CTMLE. CausalStudy.available_methods() names this item for part (d). estimators/drtmle.py, estimators/composite.py and estimators/ctmle.py refuse the other parts before any learner.

part	request	step
(a)	observation weights on the randomized missing-outcome DRTMLE	known weights in each targeting equation, with the reduced regressions and \(\pi\) fitted under weighted loss. The transport argument of the DR-TMLE supported estimands page states this step. The declared mechanism is the tilted-law mechanism only when the weights depend on \(W\) alone. The contract requires that condition. Base: Díaz and van der Laan (2017), Section 2.1 and Equation (1)
(b)	evaluation= on the randomized missing-outcome DRTMLE	a diagnostic only, as X50 part (d). No new theory is needed
(c)	the composite missing-data route for a method other than TMLE, DRTMLE and CTMLE	the indicator reduction to \(\Delta_A \cdot \Delta \cdot 1\{A = a\}\) for each method whose binary-treatment result ships. No shipped method reaches this refusal
(d)	NaturalCourseMean, PAR and PAF with complete outcomes under CTMLE or DRTMLE	the \(\Delta \equiv 1\) case of X50 part (c) and X51 part (a). With complete outcomes the natural-course TMLE returns the sample mean and the curve \(Y - E[Y]\), as the ey_obs row of the evidence map records. C-TMLE gives points only, as X51 states
(e)	baseline strata (strata=), and a declared missing treatment, under CTMLE(strategy="derivative")	one derivative fit within each stratum, as the ordinary TMLE fits its stratum estimates; a partner mechanism for the composite indicator \(\Delta_A \cdot 1\{A = a\}\). estimators/ctmle.py and estimators/composite.py refuse both before any learner and name this item

Acceptance needs each check below.

• part (d) equals X50 part (c) and X51 part (a) at \(\Delta \equiv 1\), and its natural-course coordinate equals the sample mean exactly;

• unit weights in part (a) reproduce the unweighted fit exactly;

• a nonzero witness for each changed term;

• a pre-fit refusal test for each request that stays refused;

• a registered study for each interval claim.

X63. Missing data, intermediates and designs

CausalData, LongitudinalData, the declarations of data/validate.py and data/known_mechanism.py, and the natural-course support report refuse the requests below. A missing treatment beside a continuous treatment or a categorical modified treatment policy is an invalid_declaration, not a gap. The recording may depend on the treatment, so the law of \(A\) given \(W\) is not identified. F33 keeps the composite indicator with a controlled direct effect.

part	request	step
(a)	a declared known density for a continuous treatment	a declared conditional density in place of the fitted one in the density ratio, for a policy whose definition does not read \(g\). Base: Díaz, Williams, Hoffman and Schenck (2023), Theorem 3, whose remainder is a product of the ratio error and the outcome error. A declared \(g_0\) makes the ratio error zero, as the known treatment mechanism section states for discrete policies. The curve stays valid at \(g_0\). The part claims no efficiency in the known-\(g\) model, as that section states for the ATT
(b)	a multi-valued intermediate variable	the controlled direct effect at each level \(z\), through the indicator \(1\{Z = z\}\). The step is an indicator reduction
(c)	a fit with no covariates, which includes baseline=() on LongitudinalTreatment, LongPanel and TimeToEvent	an intercept-only nuisance design. The arm mean then reduces to the unadjusted mean. No new theory is needed. The three longitudinal layouts share one container, so one refusal in LongitudinalData covers them
(d)	a support report of the response mechanism for the natural course with missing outcomes	a diagnostic over the fitted response probabilities. It makes no estimator claim

Acceptance needs each check below.

• a two-level intermediate equals the shipped binary controlled direct effect;

• a fit with no covariates equals the unadjusted arm means exactly;

• a long panel with no baseline covariate equals the equivalent wide frame exactly;

• a declared density equal to the fitted one reproduces the fitted-density fit;

• a nonzero witness for each changed term;

• a pre-fit refusal test for each request that stays refused;

• a registered study for each interval claim.

X64. Intervention and policy declarations

interventions/base.py, interventions/policy.py, msm.py and CausalStudy refuse the requests below before any learner. F33 keeps an IPSI plan with a modified-policy or risk-ratio-tilt node, an MSM weight from a learned mechanism, and automatic cumulative-bound selection for LTMLE.

part	request	step
(a)	Stochastic(density_kind="estimated"), and a user Intervention with an estimated density	the regime curve plus the term of Kennedy (2019), Appendix 8.2, Lemma 3. Kim, Kennedy and Naimi (2021), Appendix F, prove that term for a general intervention distribution. The term needs the derivative of \(g^*\) with respect to \(P\). A user-written density supplies none, so the part needs a declared family with its derivative. For a declared family it is a natural extension. For an arbitrary user density it stays refused
(b)	a policy with a continuous randomizer	an integral over the declared randomizer law. Base: Díaz, Williams, Hoffman and Schenck (2023), Section 2, journal page 849, and Theorem 3, as verdict (c) of the natural-extension verdicts reads them. The law is known, so the chain rule with a known weight carries it. The contract requires the error of the numerical integral to be \(o_P(n^{-1/2})\)
(c)	a known stochastic density on a continuous dose	the curve of Kennedy (2019), Appendix 8.2, Lemma 2: \(g^*(A \mid W)/g(A \mid W)\,(Y - \bar Q(A, W)) + \int \bar Q(a, W) g^*(a \mid W)\,da - \psi\). The contract requires \(g^*(\cdot \mid W)\) to be absolutely continuous with respect to \(g(\cdot \mid W)\), with a bounded ratio. It states the error of the integral over \(a\)
(d)	estimated MSM projection weights from arm shares, and an estimated MSM design such as a sample centre	a stacked estimating equation for the finite-dimensional weight or design
(e)	a method whose catalog does not declare the requested target	a catalog row and its evidence for each pair of method and target. The catalog row needs no new theory. Each pair inherits the readiness of the item that holds its construction. For example, CTMLE ATT stays in F5

Acceptance needs each check below.

• a continuous-randomizer declaration with two atoms equals the shipped finite randomizer;

• at an exact law, a known density equal to the true law of \(A + \delta\) reproduces the shift target;

• a declared family that does not read \(P\) reproduces the known-density fit, with a zero derivative term;

• a nonzero witness for each changed term, the mechanism term of part (a) included;

• a pre-fit refusal test for each request that stays refused;

• a registered study for each interval claim.

X65. Sensitivity analyses beyond the shipped scope

The E-value, the derived risk ratio, the omitted-variable bound and the missingness tilt each refuse the requests below. F34 keeps the E-value among the treated or the controls, and the E-value of a regime or policy contrast.

part	request	step
(a)	the standardized E-value with a response mechanism	a plug-in population standard deviation \(\{\hat E[Y^2] - \hat E[Y]^2\}^{1/2}\). It reads two natural-course means under missing at random, of \(Y\) and of \(Y^2\), each with a fixed q_bounds. The shipped conversion uses its standard deviation as a plug-in, and this part does the same. The part depends on a continuous natural-course mean
(b)	the E-value, the derived risk ratio and the omitted-variable bound of a stratum-conditional estimand	the marginal result applied inside each stratum. The step is a finite partition
(c)	the derived risk ratio for a method other than TMLE	a same-seed equality witness for each method. No new theory is needed
(d)	the derived risk ratio after fold evaluation	the fold-evaluated ratio of X61 part (c). No new theory is needed beyond that part
(e)	the derived risk ratio of a controlled direct effect	the cached retargeting passes the fitted intermediate level. No new theory is needed
(f)	the omitted-variable bound after repeats above 1	the bound computed on each draw, then the median, under the argument of X53 part (b). Each draw shares the first-order curve, so the median bound uses that curve, not a coordinatewise median of influence terms. X53 part (b) carries the TMLE point only. The contract therefore states that \(\hat\sigma^2\) and \(\hat\nu^2\) are each asymptotically linear, with common limits over the draws
(g)	a benchmark that drops every covariate	an intercept-only short model. It depends on X63 part (c)
(h)	the missingness tilt and tipping_gamma of the natural-course mean	the point curve \(E[\Delta Y + (1 - \Delta)\bar Q_\gamma(A, W)]\). The spread columns take the plugin_ names, as X57 part (d)
(i)	the missingness tilt of a ratio, a regime mean or an MSM coefficient	the tilted arm means, then the delta method for a ratio, an indicator reduction for a regime, and the fixed projection for an MSM. At \(\gamma \neq 0\) the spread columns use the plugin_std_err and plugin_interval_* names, and no interval is claimed, as in part (h) and X57 part (d)
(j)	a dose-grid support diagnostic for a continuous MSM	the fitted treatment density at each grid dose, with the share of rows below a declared floor. It is a diagnostic

Acceptance needs each check below.

• one stratum in part (b) reproduces the marginal result exactly;

• one repeat in part (f) reproduces the shipped bound exactly;

• a nonzero witness for each changed term;

• a mutation control for each part that adds a term;

• a registered study for each part that reports a confidence limit.

X66. Simulated confounding beyond X47 and X48

The base law is the pinned DoWhy refuter, as in X47. Each part below needs a declared reading of the strengths. No part makes an interval claim. The simulated-confounding request checks in sensitivity/ refuse each request before any refit.

part	request	step
(a)	an MSM with a link other than identity, log or logit	the replay refits the MSM under its own link. The law does not read the link
(b)	a regime class other than Static, Rule and Stochastic	the replay of a regime that is a known function of \(W\). A user Intervention with density_kind="known" qualifies
(c)	a fixed regime or MSM beside another axis	a replay of each axis of the joint fit. It depends on X57
(d)	a risk-ratio tilt fit	the contract declares one of the two shipped readings. The replay can rebuild the mechanism on each perturbed draw, as the incremental replay does. It can also apply the known rule to the perturbed treatment, as the policy replay does. RiskRatioTilt is a known rule: the lmtp ipsi rule, with a known two-point randomizer on the natural value
(e)	a binary replay under a method other than TMLE, CTMLE and DRTMLE	a refit of the stored estimator on each perturbed draw, with a zero-strength reproduction witness for each estimator
(f)	a continuous replay under a method other than TMLE	as part (e). A continuous fit under DRTMLE or CTMLE needs F5 first, because neither method fits a continuous dose
(g)	a fixed-policy replay under a method other than TMLE, DRTMLE and CTMLE	as part (e). X50 and X51 hold the DR-TMLE and C-TMLE regimes and MSMs
(h)	PAR or PAF under DRTMLE or CTMLE	as part (e). It depends on X50 part (c), X51 part (a) and X62 part (d)
(i)	a binary replay of a parameter off the arm axis, and a continuous replay of a parameter off the policy axis	the replay applied to the refit of that parameter, with a declared reading for each parameter. A parameter that reads \(g\) follows part (d)

Acceptance: the replay at zero strength reproduces the estimate; a nonzero witness for each part.

X67. Refutation and assessment adapters

refute and bootstrap_measurement_error refuse the requests below. Each part needs a generated-outcome process whose effect is exactly computable from its generated law. Such a part needs an exact calculation and no new theory.

part	request	step
(a)	a longitudinal refute adapter and a longitudinal generated-outcome process	a sequential outcome process that reads the baseline covariates and the treatments only, or one that also generates each time-varying covariate. Then the sequential g-formula on the generated law gives the effect exactly
(b)	a generated-outcome process for another outcome family or a non-binary treatment	a registered process for each family and for each pair of arms
(c)	a generated-outcome process for a controlled direct effect, an MSM, an intervention, a ratio, or a functional other than BackdoorMeanContrast	a registered process for each target, with its effect computed exactly. An intervention that reads the propensity, such as an odds tilt, needs a process that also generates the treatment
(d)	a generated-outcome process with missing outcomes	a declared observation process under missing at random, and the effect computed on the complete law
(e)	bootstrap_measurement_error on a result that is not a point-treatment result, or on the strata variables	a perturbation of each node’s covariates, and a declared reading that keeps the reported strata at their recorded values

Acceptance: each process’s effect checked against an exact calculation; a pre-fit refusal test for each request that stays refused.

X71. Repeated outcomes for the sequential baselines

SequentialGComputation, SequentialIPW and ParametricGFormula refuse a repeated outcome, declared with outcome=Repeated([...]), before any learner. LTMLE fits one: each horizon is the end-of-study fit of the panel truncated after it (repeated outcomes). The same reduction applies to each baseline, and its stacked estimating equation covers several horizons as it covers several plans.

part	what to add	evidence
(a)	gcomp and ipw in REPEATED_OUTCOME_KINDS, with the per-horizon fit of the truncated panel	tests/unit/test_repeated_outcome_subclasses.py requires each horizon’s estimate and curve to equal the end-of-study fit of the truncated panel
(b)	parametric_gformula in REPEATED_OUTCOME_KINDS, with one simulation of the truncated panel per horizon. Each horizon fits the covariate and outcome models of its own truncated panel	the same reduction test, which exempts ParametricGFormula until this part ships

Acceptance: the exact reduction test for all three estimators, and a registered property study of the repeated-outcome cells.

X72. Static regimen values from structural blips with time-varying features

StructuralNestedMean fits blips whose features read baseline columns, earlier treatments and time-varying covariates. A feature that reads a time-varying covariate allows the blip coefficients and the reference mean ey_reference only. The estimator refuses a static level, a static contrast and check_model for such a fit with IMPLEMENTATION_GAP and this item.

The static value needs the regimen mean of the feature, \(E[\phi_t(H_t(\bar a))]\). That mean depends on the law of the covariates under the regimen, which the estimator does not fit. Lewis and Syrgkanis (2021), supplement Lemma 6, identifies the value from the blips and that law. Their arXiv version, Corollary 9, gives the inference. The proceedings version has no such result.

part	what to add	published source
(a)	static levels and contrasts when a feature reads a time-varying covariate	the supplement, Lemma 6, and the arXiv version, Corollary 9
(b)	a stack of the blip coefficients with the LTMLE intermediate means \(E[\phi_t(H_t(\bar a))]\), as an alternative route to part (a)	a natural extension of the sequential regression of LTMLE
(c)	the model check for the contrasts of parts (a) and (b)	the same joint Wald construction as the shipped check

Acceptance: a written derivation of the influence curve under the Eligibility conditions, an exact-law witness whose feature reads a covariate with a nonzero effect on the contrast, a mutation control that drops the covariate-law term, and a registered study cell.

X74. Assessment and study integration for the structural nested mean model

StructuralNestedMeanResult declares fitted_method = "snmm" and no assessment_family. cleverly.assessment.assessment_capabilities therefore raises a bare TypeError that names the missing family. CausalStudy offers no method that fits StructuralNestedMean.

part	what to add	evidence
(a)	an assessment_family for the result, with one declaration per assessment operation. Each declaration is available, or refuses with a reason code and a roadmap id	a test that every operation of assessment_capabilities runs or refuses with a code and an id on a structural fit
(b)	a CausalStudy method for the estimator, whose study report carries the structural label	a study test that the label reaches the study report

Acceptance: both tests, and a refusal for each operation that a structural fit cannot support, such as a truncation curve, which an estimator with no inverse probability has no use for.

X76. Studies of the targeting and fitting options

These options run, and each fit that declares one carries the experimental label. No registered study measures a fit that uses them. src/cleverly/estimators/_option_support.py writes each condition.

part	option	what a study measures
(a)	stopping="scaled_var" and "sample_size", point and longitudinal	interval coverage at the residual the rule leaves, beside the coverage bound the summary prints
(b)	outcome_by_arm=True	bias and coverage with one outcome regression per arm
(c)	patience= on the cross-validated C-TMLE path	bias and coverage when the counter stops the path early
(d)	treatment_adjustment=	bias and coverage under the declared restriction, with a correct mechanism model on the subset, and with a dropped covariate that affects only the treatment

iterate="best" and step_bound= under stopping="relative" keep the support of the fit. That walk stops only at the solution of the score equation, to tol.

Acceptance: a registered study per part, with its red cells reported, and a support row that names the option.

X73. Pooled-over-time parametric g-formula models

This row has two parts. Part (a) adds pooled models. Part (b) adds a vector treatment node with a dose component.

ParametricGFormula fits one model per node and covariate. gfoRmula and pygformula fit one pooled model per covariate over all time rows, with lag and cumulative-average terms of the history. A pooled model restricts the node-specific models, so it needs fewer parameters and it extrapolates over time. This row adds the pooled form to the shipped estimator.

what to add	evidence
a pooled GLM for each covariate and for the outcome or hazard, fitted on long rows. Each row carries the time, the lag and the cumulative-average terms of the history that the caller declares. The score of a unit is the sum over its rows, and the information is the sum over all rows. The stacked equations, the score-function derivative and the simulation error stay as in the shipped page	exact laws on which the pooled model is correct, with the complex-step Gateaux check of the curve, and a mutation control that scores each row as a unit. A nonzero witness for each history term

Acceptance: the exact-law witnesses of the pooled model, the mutation controls, and a registered study cell for a law with a lag term.

ParametricGFormula refuses a mixed treatment node today (GFORMULA_MIXED_NODE_REFUSAL). A mixed node holds a categorical component and a dose, and the simulation draws one natural treatment column per node.

what to add	evidence
(b) a joint natural-treatment model of a mixed node: the categorical component first, then each dose given the component, with the score of each factor in the stacked equations. The draw of a JointPolicy reads the drawn components	exact laws with a mixed node, the complex-step Gateaux check of the curve, and a mutation control that drops the dose factor’s score

X75. Data-tuned policies beyond the shipped tuned caps

The shipped data-tuned caps tune one cap at a continuous node on training rows. Each fit refuses the compositions in the table below before any learner. The refusals name this item.

part	request that stays refused	what it needs
(a)	a tuned cap at a node with dose atoms	the mixed-law ratio at the cap, and the derivative term of the tuned cap at an atom
(b)	a tuned cap with baseline strata	a cap fitted within each stratum, and the target that averages the stratum parameters
(c)	a tuned cap with a missing treatment or a missing outcome	the observation weights in the tuning loss, and the influence curve with the tuned cap
(d)	a tuned cap with an intermediate	the tuned cap in the controlled direct effect, and its derivative term
(e)	a policy fitted to the analysis sample other than a declared tuned cap	a declared target for the fitted policy, and its derivative term
(f)	a fold-average target with a declared stopping rule, step bound or best iterate	the declared rule in each fold’s intercept fluctuation

Acceptance: a pre-fit refusal test for each request that stays refused until its part ships. Each part that ships needs an exact-law check with a nonzero witness for the derivative term.

X77. Censored data for continuous price policies

A longitudinal fit of a continuous-node policy with a censoring factor runs. It carries the experimental label. The mtp-pricing study draws complete data, so its support rows cover complete data only (src/cleverly/_support_rows.py). The longitudinal rows of categorical treatments cover censored fits.

what to add	evidence
a censoring draw on the mtp-pricing law, with the censoring factor learned beside the classifier price ratio	a registered study cell per engine at three nodes, with its red cells reported, and support rows with missing=("censoring",)

Acceptance: the registered cells, and a support case in tests/studies/support_cases.py. This row ships after the beta release (owner decision, 2026-10-16).

P1. EP learner

Van der Laan, Carone and Luedtke (2024), arXiv:2402.01972, govern this item. After first-hand review of their EP derivation, add ConditionalContrast estimands, modifier schema, sieve/basis strategy, efficient plug-in risk and targeting, bounded outcome predictions, a second-stage contrast learner, out-of-fold risk/calibration, and a conditional prediction result. Reuse study/identification objects, nuisance strategies, folds, data backends, provenance, persistence, and capability-aware assessment.

The first catalog is paper-derived CATE and conditional relative risk. Other losses and contrasts require their own derivations. Aggregating an EP curve is a separate parameter and receives scalar inference only after its influence contribution is implemented and tested.

Acceptance requires exact score and risk checks, bounded predictions, out-of-fold calibration, modifier and split/basis stability diagnostics, mutation controls for targeting sign, basis contribution, and contrast construction, plus registered oracle-efficiency and stability studies.

R1. Nested Riesz engine and initial catalog

Purpose and scientific boundary

Add the general nested Riesz engine as one scientific review unit. Direct Riesz learning replaces the analytic construction of a representer from propensity or density components; it does not generally replace the outcome regression. The single-stage form remains a plug-in term plus alpha * (Y - f). Engine expressibility is not permission to register a causal target.

The governing nested-TMLE source is Balkus, Testa & Hejazi (2026), arXiv:2604.21721v1: Theorems 1–2, Algorithm 1, and Sections 4 and 5. Chernozhukov, Newey & Singh (2022), Econometrica 90(3), governs the direct representer moment problem and product-bias identity. RieszCML is pinned only as secondary implementation evidence; paper/code discrepancies must be recorded and tested.

Stages are stored innermost first, matching the order the backward recursion executes in. Two nearby orderings run the other way and neither is the storage convention. Theorem 2 indexes outermost first, so the paper’s prefix product is a suffix product here:

paper order:       outer 1, ..., inner T
stored order:      inner 0, ..., outer J-1

And longitudinal/sequential.py reverses its steps before returning them, so the stored SequentialStep tuple is time-ascending. steps[0] is the outermost stage whose targeted prediction is averaged into the estimate. Do not mirror it. Every public description, serialized manifest, fixture, and diagnostic names the storage direction.

Contracts and public surface

Introduce immutable advanced contracts under a Riesz namespace.

contract	what it declares
FunctionalStage	the regression, plug-in map, representer problem, intervention evaluation, residual source, identification metadata, targeting map, stage name, and history
NestedFunctional	ordered stages, evidence ID, output shape, parameter key, and causal metadata
AnalyticRepresenter, DirectRiesz, ProvidedRepresenter, internal ComposedRepresenter	the mechanism-derived, directly learned, externally supplied, and cumulative stagewise representers
fitted stage artifacts	observed and intervention regression predictions, alpha, alpha_star, component and cumulative products, residual sources, masks, folds, targeting coefficients, losses, balance diagnostics, row identity, and training provenance
RieszTMLEMethod	a scalar RieszResult satisfying CausalResult and the shared inference, contrast, identification, assessment, persistence, and provenance protocols

A custom statistical functional may use NestedFunctional. Causal prose and intervals need a registered evidence ID and a complete influence construction. RieszTMLEMethod never fabricates a propensity object for a direct fit.

A provided representer must establish row identity, folds, training provenance, and counterfactual evaluation. Missing alpha_star is refused rather than replaced by observed alpha. Built-in estimands construct stages internally; advanced custom builders validate roles, shapes, histories, intervention evaluation, and identification metadata before fitting.

Folds, fitting, and targeting

Use one validated outer fold plan for regression and representer fits. Each row is predicted only by models not trained on it; learner tuning remains inside the outer training fold; supplied folds must prove coverage, disjointness, grouping, cluster integrity, and row identity. Independent nuisance folds remain unavailable until their theory and diagnostic implications are specified.

For stored stages 0..J-1, innermost first, construct:

omega_observed[j] = product(alpha[k], k=j..J-1)
omega_plugin[j]   = alpha_star[j] * product(alpha[k], k=j+1..J-1)

The plug-in product changes only the current stage to its intervention state; it is not a product of every alpha_star. Store all components separately. Fit initial regressions from the observed outcome outward, fit or construct each stage’s observed and intervention representers on the same training fold, and pass each plug-in output outward as the next target.

A direct strategy solves an explicit empirical Riesz moment problem. A generic supervised regression of an estimated inverse propensity score is not a direct-Riesz implementation and is not labelled one. It is the nearest wrong construction, and it fits and predicts without complaint.

Target innermost first. Solve the fluctuation with omega_observed[j], update observed predictions with that product and plug-in predictions with omega_plugin[j], and pass the targeted plug-in outward. Identity and logistic fluctuations are supported initially. Logistic targeting requires a validated scaler and preserved bounds; a degenerate direction raises CleverlyError.

The targeted uncentered curve is:

outermost_targeted_plugin
+ sum_j omega_observed[j] * (
      targeted_residual_source[j] - targeted_observed_regression[j]
  )

Center it at the targeted plug-in estimate, then apply declared Hájek weights, outcome scaling, cluster aggregation, covariance, smooth contrasts, and simultaneous inference through existing infrastructure. Recompute stage scores and the complete influence-curve mean from stored arrays. Do not use an untargeted curve for a targeted estimate’s standard error.

Repeated splitting follows only after a single split is correct. Take marginal medians over repeats with the registered split-dispersion variance. Retain repeat IDs on artifacts. Refuse joint covariance where coordinatewise medians break identities. Reject equal-fold averaging with an unequal-fold-size test.

Initial catalog and refusals

The implementation PR must support each initial cell with full evidence or retain its named pre-fit refusal.

typed estimand or design	analytic Riesz	direct Riesz	decision
point CounterfactualMean	yes	yes	canonical single-stage functional
point ATE	yes	yes	joint contrast of counterfactual means
point RiskRatio and OddsRatio	yes	yes	existing joint delta method; binary outcome only
point outcome missing at random	yes	yes	missingness stage composed with each treatment-specific mean
longitudinal static and dynamic RegimeMean	yes	yes	evidenced sequential instances after history and arm mutations pass
longitudinal RegimeContrast	yes	yes	joint contrast of evidenced regimen means
point ModifiedTreatmentPolicy	yes	yes	evidenced invertible policies with target-specific moment map
smooth contrasts of initial rows	yes	yes	existing delta-method infrastructure
ATT and ATC	gated	gated	ratio or conditional-functional stage and variance audit required
NaturalCourseMean, PopulationAttributableRisk, and PopulationAttributableFraction	gated	gated	composition and parameter-key audit required
one-point stochastic RegimeMean	gated	gated	density-valued direct-loss audit required
IncrementalMean and IncrementalEffect	refused	refused	intervention depends on the treatment mechanism
point or longitudinal MSMProjection	gated	gated	target-specific projection and coefficient-EIF adapter required
mediation and ControlledDirectEffect	refused	refused	outside the first catalog
survival and competing-risk results	refused	refused	separate at-risk/event audit required
arbitrary custom nonlinear functional	refused as causal	refused as causal	statistical label only after validation

Analytic Riesz is the existing evidenced mechanism-derived estimator expressed through the new contract. Its gate is identity with the normalized existing engine for targeted predictions, influence curve, standard error, and interval. Point estimate parity alone is insufficient.

Diagnostics and persistence

Default cheap validation covers stage scores, influence-curve mean, direct objective improvement, held-out moments, representer tails and leverage, regression loss, and fold/provenance integrity. Analytic fits may report mechanisms and truncation; direct fits report representer loss, balance, tails, leverage, regularization, and clipping; composed fits report components and products. Direct-only fits must not reconstruct a propensity model for diagnostics or sensitivity.

Store ordered stage definitions and evidence IDs, every fitted array, reconstructible strategy configuration, fingerprints, settings, structured identification and parameter keys, cached reports, and replayability. Unknown types fail allowlist decoding. Custom callables are descriptive and non-reconstructible; cache-only operations remain possible only when stored predictions and provenance suffice. Losing alpha_star, stage order, or component products is a load error. Round trips compare every artifact, score, diagnostic, estimate, influence curve, metadata record, and cached assessment.

Evidence and implementation sequence

Every registered functional needs the full instrument set. That is exact finite-support laws, Gateaux derivatives, and product remainders with both nuisance errors nonzero. It is also score checks, union-model witnesses where derived, and nonzero targeting. The mutations are sign, alpha_star, stage and product order, mask, and counterfactual. Leakage spies, analytic regressions, and a pinned secondary fixture complete it. Direct fits additionally require loss improvement, held-out moments, same-fold observed and intervention predictions, provenance, and extreme-representer diagnostic response.

Nested evidence uses nonconstant two- and three-stage laws and rejects reversed stages, reversed products, all-starred products, wrong signs, and masks. Missingness evidence makes observation depend on treatment/history and proves unobserved rows receive the correct plug-in update. Longitudinal evidence covers dynamic-history restriction, third-arm categorical mutations, treatment/censoring products, clusters, repeats, and persistence. Registered studies cover point means/ATE under both union-model halves, direct consistency and coverage, static/dynamic regimen means, and weak overlap with thresholds fixed before the final run.

Implement in one review PR with gated commits: contracts and pre-fit refusals; analytic single-stage parity; direct single-stage learning; nested and missingness composition; longitudinal adapters; then persistence, assessment, documentation, and the secondary fixture. No commit merges independently. Handoff requires the enabled/refused catalog, source locators, implementation revision and discrepancies, evidence instruments, local commands/results, and path-based reasons for omitted validation studies.

R2. Evidence-gated Riesz catalog expansion

Expand target by target after the engine lands. Mediation, additional longitudinal targets, sampling designs, and other nested functionals each require a governing derivation, typed adapter, registry entry, evidence row, refusal boundary, documentation, and applicable statistical study. Do not expose a generic engine capability as a certified causal estimand.

Future investigation contracts

Each contract below states the kept claim, the kind of argument that it needs, and the boundary that ships. The hard-stop review gives the sources read for each verdict.

F12. Missing-outcome simulated-confounding replay

The pinned DoWhy refuter perturbs the treatment and the outcome only. X47 part (e) holds a declared response mechanism that reads the covariates only. There \(\Delta \perp (A', Y') \mid W\) holds, so missing at random holds given \((A', W)\).

kept claim	kind	missing argument
a replay of the stored estimator when the response mechanism or the treatment-observation mechanism reads the treatment	identification	a flip of \(A\) breaks missing at random given \(A'\), so the stored estimator does not identify the perturbed law. A refit that carries the original \(A\) as an auxiliary variable of the response model identifies it, because \(\Delta \perp Y' \mid (A', A, W)\). That refit is a different estimator and needs its own contract

F13. Longitudinal simulated-confounding replay

The pinned DoWhy law is a single-time-point perturbation. X48 holds one time-fixed latent on uncensored terminal-outcome fits with no time-varying covariate after the first treatment node.

kept claim	kind	missing argument
censoring or a survival outcome	identification	the flip breaks coarsening at random at each censoring node, as in F12. An additive shift of an absorbing process is not a law on its support
a time-varying covariate after the first treatment node	identification	a covariate generated under the original \(A_t\) depends on the latent given \(A'_t\), and the sequential regression conditions on it
a later treatment node whose mechanism reads an earlier treatment	identification	the node was generated under the original earlier treatment, so given the misclassified one it depends on the latent. X48 moves it only when its contract defines that induced association, or restricts the mechanisms to ones that do not read an earlier treatment
a time-varying latent with treatment feedback	identification	a law whose strengths name the feedback. Tan (2025), arXiv:2308.15725v1, Equations (11) and (34), gives bounds and no law

F15. Controlled-direct-effect simulated-confounding replay

X47 part (f) holds the outcome-axis cells, and an intermediate-axis law that flips or shifts \(Z\) and shifts \(Y\) with \(A\) held.

kept claim	kind	missing argument
the treatment axis on a fit with an intermediate	identification	a flip of \(A\) makes the latent confound \(Z\) and \(Y\) through the misclassified \(A\). No law names the strength of that path. mediationsens 0.0.3 simulates a pretreatment latent for natural effects only

F26. Confidence limits of the plug-in omitted-variable bound

nu2_estimator="plugin" estimates the Riesz second moment as \(E_n[\hat\alpha^2]\). That value moves at first order with the fitted treatment mechanism, because \(E[\hat\alpha^2] - \nu_0^2 = 2E[\alpha_0(\hat\alpha - \alpha_0)] + E[(\hat\alpha - \alpha_0)^2]\). Its curve \(\hat\alpha^2 - \hat\nu^2\) has no term for that fit.

On tests/discrete_law.py with the oracle nuisances, that curve differs from the Gateaux derivative of \(\nu^2\) by up to 21.3 for the ATE and 45.9 for the ATC. Chernozhukov et al. (2018), arXiv:1608.00060v7, Section 1.1, record that bias for a non-orthogonal plug-in. DoubleML calls its plug-in fallback non-orthogonal.

kept claim	kind	missing argument
confidence limits of the plug-in bound for a learned mechanism other than the declared model of X26	regularity	a learner-specific argument, such as an undersmoothing rule, that removes the first-order term. No standard step carries it

The orthogonal estimator is the alternative. nu2_estimator="doubly_robust" estimates \(\nu^2\) through the orthogonal score of Chernozhukov, Cinelli, Newey, Sharma and Syrgkanis, arXiv:2112.13398v5, Section 4, Lemma 2. The repository’s earlier citation of version 6, not re-read here, numbers that lemma Lemma 3. Their Theorem 4 gives the limits for any mechanism learner at its rates. The refusal names this alternative. X26 holds the declared unpenalized logistic or multinomial mechanism and the declared known mechanism. A Super Learner that contains that model stays here, because the bound reads the fit’s own \(\hat g\).

F2. Targeted bootstrap inference

The package ships the full-refit bootstrap, in which each replicate refits the whole estimator. Its registered study full-refit-bootstrap-and-derived-contrasts measures in-sample fits with correctly specified nuisances, and it measures the point-treatment TMLE only. TMLE publishes the percentile interval as inference for an in-sample point-treatment fit only. A cross-fitted point-treatment fit prints its bootstrap as a diagnostic, as the cross-fitted longitudinal kinds do. Every DRTMLE fit and every CTMLE fit prints it as a diagnostic too. An in-sample TMLE fit with a data-adaptive learner still publishes the interval. The registered study measured only correctly specified nuisances, and this row holds the theory for the data-adaptive case.

kept claim	kind	missing argument
full-refit bootstrap consistency with data-adaptive or cross-fitted nuisances	asymptotic	Tang and Westling (2024), arXiv:2404.03064v2, Theorem 3.4, needs condition (B2) for the bootstrap nuisance, and the paper does not treat cross-fitting. A resample can put copies of one row in a training fold and its validation fold
a row-resampling (nonparametric) targeted bootstrap for learners other than HAL	asymptotic	Cai and van der Laan (2020), arXiv:1905.10299, Theorem 4, covers a HAL learner with the bound \(C\) fixed. Coyle (2017), Theorem 9, covers a model-based bootstrap under a uniform Donsker class. No read source covers the nonparametric bootstrap with another learner

X55 holds the in-sample bootstrap with finite-dimensional nuisances, the HAL-TMLE bootstrap, and the model-based targeted bootstrap of Coyle (2017), Theorem 9, under a uniform Donsker class. Resampling stored curves, retargeting cached arrays and refitting the complete estimator are distinct procedures. Do not infer one from the name of another.

F16. Longitudinal sensitivity-bound estimation

Tan (2025) derives population sensitivity bounds for a terminal outcome under binary, static longitudinal strategies. The table gives the three kept claims.

kept claim	kind	missing argument
(a) a sample estimate of the bounds	asymptotic	the consistency of a nested sample program with generated pseudo-outcomes at each period. Tan, arXiv:2308.15725v1, Section 3.1, leaves estimation with sample data to future work. Shen, Bacak and Kennedy, arXiv:2601.17779v1, Section 5.2, do the same for the incremental analogue
(b) an interval for that estimate	regularity	sampling inference for non-smooth bound functionals over periods. Bonvini et al., arXiv:2210.04681v2, Section 6.1, leave the time-varying constraint to future work
(c) an omitted-variable bound or an E-value on a longitudinal fit	identification	a per-period latent law that identifies the bias of a sequential g-formula target. The bound of Ding and VanderWeele (2016) reads a point exposure. Chernozhukov et al., arXiv:2112.13398v5, Section 4, bound a functional of a known regression form

Both longitudinal refusals cite this item.

F7. Time-respecting cross-fitting

Blocked-temporal and rolling-origin folds wait for a published TMLE result whose dependence assumptions match the supported data. The kind of missing argument is serial dependence. Ballinari and Wehrli (2024), arXiv:2411.10009v2, Theorem 4, and Semenova et al., arXiv:1712.09988v6, give DML results under mixing, not TMLE results. The result must specify which rows may train each prediction and which asymptotic argument licenses the interval. Ordered indices passed through iid fold machinery are not sufficient.

F18. Selector-path C-TMLE inference

The greedy, ordered, discrete, lasso and learners paths report point estimates and path diagnostics. They refuse ci, pvalue and std_error under the working_mechanism_plugin status. They report the ordinary curve at the selected candidate as plugin_std_error and plugin_interval. That curve does not establish conditional or unconditional coverage after selection. F18 reopens inference when a published result supplies the influence function and covariance after the shipped selection.

A result that reopens a selector path, including lasso and learners, must bound the adaptive-mechanism term, or Ju et al. (2018)’s \(\Delta(P_1)\), without conditioning on the pair \((\bar Q_n, \bar Q_0)\), or must show that the term is a product. A term that is linear in \(g_n - g_0\) when \(\bar Q\) is wrong does not qualify.

X52 part (a) holds one declared partial candidate with parametric learners, where a stacked estimating equation carries the fixed candidate. This item keeps inference after the stopping-index selection. Its kind is adaptive-optimum inference.

C-TMLE0 (strategy="derivative") ships with the TMLE status under a consistent outcome regression (C-TMLE0). The collaborative reading of Ju et al. (2018), Section 5.3, for an inconsistent outcome regression stays here.

F18 also keeps a fold-specific selection and update on the selector paths, which cv_evaluation=True and targeting_scheme="fold" request. No read source derives one. CTMLE refuses both before any learner, and the refusal names this item.

F18 is not a natural extension under the Eligibility rule. The selector is a data-adaptive selection step, which the rule names as one with no established argument. No published base exists for one stopping index shared across arms.

The fixed-candidate curve comes first. The curve is unproved when the candidate’s mechanism limit differs from the treatment law. On make_instrument(n=2000, seed=44), an intercept-only working mechanism gives a standard error of 0.0441. The sampling standard deviation of the numerically identical least-squares coefficient is 0.0538. Over 300 greedy fits the ratio is 0.844, and nominal 95% intervals cover in 0.92 of fits. TestTheWorkingMechanismDiagnosticMissesTheExactVariance in tests/unit/test_ctmle.py pins the gap.

Ju, Benkeser and van der Laan (2020), Theorem 1 in Section 3.4 of arXiv:1806.06784v3, show the form a correction can take: the ordinary curve at the propensity limit minus a term \(D_r\) that vanishes at the true propensity. Their construction differs from the shipped selector. A result must settle this fixed-candidate case before it addresses selection. X52 part (a) settles it for parametric learners only.

Sources read, and why none closes F18. The source audit gives each locator.

source	what it gives	what it lacks for F18
van der Laan and Gruber (2010), Section 4	an abstract adaptive-mechanism contribution under fixed-limit and regularity assumptions. Section 4.3 leaves cross-validation over-selection open	the curve after the shipped stopping-index selection
Ju et al. (2018), Lemma 2	a continuous-path contribution that is zero in one correct-outcome, product-rate regime. Corollary 4 gives the LASSO-C-TMLE expansion, whose extra term Lemma 2 makes zero under a consistent outcome regression and product rate. The paper gives no estimator of it otherwise. The shipped lasso path lies outside its conditions	a discrete stopping index
Ju, Gruber et al. (2019), SMMR 28(2); Ju, Wyss et al. (2019), SMMR 28(4); Ju, Schwab and van der Laan (2019), SMMR 28(6)	ordinary EIF intervals. The last reports standard errors smaller than the sampling spread	a post-selection theorem
Cui and Tchetgen Tchetgen (2024), arXiv:1911.02029v6, Theorems 5.1 and 5.2	an oracle inequality and selector consistency. Section 6 calls a Wald interval at the selected learners “completely blind to the model selection step”	a limit law
Liu (2018), Harvard dissertation, Chapter 2	asymptotic laws for C-TMLE coefficients and risks, with known candidates, known outcome variance and a known covariate law, for one binary treatment-specific mean	learned nuisances, the discrete stopping rule and joint targets
Leeb and Pötscher (2006, 2008)	no locally uniform distribution estimation after model selection in finite-dimensional regression	a transfer to this selector
Loftus (2015); Markovic, Xia and Taylor (2017)	selective inference when the selection event is quadratic and Gaussian, or the criterion and target are jointly Gaussian	either property for a targeted-loss selector
van der Laan, Carone, Luedtke and van der Laan (2026), arXiv:2307.12544v2, Section 2.2; adaptive debiased machine learning v2. The review did not read Theorem 5 or Corollary 1	inference after data-driven model selection when the selected model approximates an unknown, fixed oracle submodel	a fixed oracle submodel for the shipped path, and a proof that one global depth from nested targeted-loss folds meets the conditions of that framework
Qiu, Luedtke and Carone (2021), arXiv:2003.01856v2, Theorem 4 in Section 4.4	the ordinary influence function after cross-validation selects a sieve dimension, under Condition C5 at every candidate	a targeting step along a propensity path
Dang, Tarp, Abrahamsen et al. (2025), Journal of Causal Inference 13:20240041; Bibaut and van der Laan, arXiv:1706.07408v2, Theorems 1 and 2	a selector trained inside each fold, with a nonstandard limit	this criterion, target and shared stopping index
Rothenhäusler (2024), Electronic Journal of Statistics, Section 3.4, Theorem 2. The preprint arXiv:2008.12892v2 numbers it Section 3.5, Theorem 4	intervals after a choice among a fixed finite set of estimators, “usually not uniformly valid”	a fixed set. The shipped path is built from the data
Schnitzer, Lok and Gruber (2016), Section 5.3 and Table 3	simulated under-coverage of ordinary curves for TMLE and C-TMLE with Super Learner	a construction

Three further sources were read from their abstracts only: Schnitzer, Sango, Ferreira Guerra and van der Laan (2020); Zrnic and Jordan (2023); and Van Lancker, Díaz and Vansteelandt (2024), arXiv:2404.11150v2.

Routes that a result can take.

route	what it needs
a uniform expansion	every candidate has the same deterministic curve \(D_0\), with \(\widehat\psi_{n,k}-\psi_0=(P_n-P_0)D_0+r_{n,k}\) and \(\max_{k\leq K_n}\lVert r_{n,k}\rVert=o_p(n^{-1/2})\). Substitution of any data-dependent \(\widehat k\) then keeps the expansion, and Cramér–Wold gives the vector result at a fixed number of arms. It is plausible when every candidate converges fast to the same nuisance limits, and not under one-sided robustness
selector stability	a unique oracle candidate, a risk margin, uniform risk convergence, and a stable covariate identity at each depth. An oracle risk inequality alone proves none of these. Shao’s linear-model result shows that prediction-efficient fixed-fold cross-validation need not select consistently
a construction change	select the depth inside each outer training fold, and evaluate on its held-out rows only. Orthogonal-score arguments then treat the selector as nuisance learning, under its rate conditions
a data-adaptive target	honest splitting permits any target generation, and the same-sample theorem needs a uniform expansion, Donsker control and curve convergence. Either regime concerns a data-adaptive estimand, not the fixed target that the package reports

The oracle projection’s efficiency bound is typically smaller than the nonparametric bound. A result could therefore confirm the current curve or require a different one.

Acceptance.

• The result covers the selected index and the selector’s three split layers: outer nuisance folds, selection folds and inner selection-training folds. Learner folds and repeat draws are separate layers.

• It establishes whether the current curve suffices or an added contribution is needed. It states the remainder, the rate conditions and the covariance for every supported target vector.

• Each analysis regime is its own proof cell. An iid, complete-outcome, unweighted, unstratified, single-repeat result certifies only that cell. Missing outcomes need the response-mechanism terms, fixed weights a weighted empirical-law result, estimated weights their first-stage contribution, clusters a cluster-level expansion, strata stratum-specific expansions and their joint covariance, and repeats the median and split-dispersion aggregation.

• The multi-arm case picks one stopping index for every arm. A result gives the full vector influence function and its cross-covariance with the ordinary curve, and it differentiates the reduction of the target vector to one scalar risk. A per-arm copy of a binary correction does not recover those terms.

• A new contribution propagates through pointwise and simultaneous inference. The evidence needs a fixed-candidate reduction and repeated-sampling coverage where the chosen candidate changes. Each repeat keeps its path and its selected index.

• Red-cell owners names the cells of the point-treatment and multi-arm selector studies, and of the candidate-sequence study’s selector_necessity family, that must pass.

F19. Outcome-adaptive C-TMLE generated-design inference

Outcome-adaptive C-TMLE selects no candidate. Its shared design, oat_design="shared", fits one categorical treatment mechanism on the estimated vector of arm-specific outcome predictions. Its per-arm design, the default, fits one binary mechanism per arm on that arm’s own prediction. Every oat fit takes the generated_design_plugin status, including an ey1-only request and a per-arm fit with strata=, delta= or treatment_delta=. ci, pvalue and std_error refuse, and plugin_std_error and plugin_interval keep the ordinary adaptive-propensity diagnostic. This item holds the interval of the per-arm strata and missing-data fits as well. Their observation factors are generated regressors in the same sense.

The cross-fitted fit follows the paper’s fold-local nuisance nesting. One outcome model, fitted on fold v’s training rows, creates both sides of that fold’s generated design. The adaptive propensity is fitted on the training side only, and both nuisances are evaluated on the held-out side. A mutation test changes every evaluation outcome without moving either nuisance on those rows.

X58 holds the per-arm design with a regular parametric outcome model: a corrected curve, its covariance and its Wald interval under a declared support predicate. Part (a) shipped, and parts (b) to (d) stay open. X52 part (b) holds the composite per-arm cells, and part (c) holds the shared design with a parametric outcome and design. This item keeps five claims. The table gives the kind of argument that each one needs.

kept claim	kind of missing argument
a flexible outcome learner. The Riesz representer of the generated-design term reads \(1/g_0\)	asymptotic
a nonparametric shared multinomial design	regularity
the cross-fitted construction. Appendix D states no theorem	asymptotic
the \((1/V)\sum_v\) fold average under cv_evaluation=True, and a fold-specific update under targeting_scheme="fold". Appendix D outlines the fold average and states no theorem. CTMLE refuses both before any learner	asymptotic
local uniformity over the nonparametric model	asymptotic

The published base. Benkeser, Cai and van der Laan (2020), Statistical Science, Theorem 1, proves under six regularity conditions that the ordinary curve needs no first-order generated-design term for one binary treatment-specific mean. This item names each appendix by its letter in arXiv:1901.05056v1. Appendix D builds a binary ATE with both arm predictions and one signed fluctuation coefficient, states no theorem for it, and outlines a pooled-validation CV-C-TMLE. The article points to Appendix G for the conditions of Theorem 1, and Supplement A labels them Appendix F. The references entry records the mismatch.

The per-arm design’s generated-design term. The per-arm design is Theorem 1’s construction for each arm. Theorem 1 needs its condition (v), which bounds the derivative of \(P(A = a \mid \bar Q_n, \bar Q_0)\) in \(\bar Q_0\). For a root-\(n\) outcome regression on a continuous \(W\), that derivative grows like \(n^{1/2}\), so the remainder \(R_{24}\) is first order.

For a parametric outcome model, the term is \(c^\top \mathrm{IF}_\beta\), with \(c = E[(1 - g_0 / G)\, \partial \bar Q / \partial \beta]\), when the design learner is consistent for \(G = P(A = a \mid \bar Q(a, W))\). With a parametric design learner, the \(\epsilon\) and \(\gamma\) terms also enter. X58 part (a) derived and implemented the complete term for the admitted configuration. The x17 ratios below measure the omission on one law. They do not show that it is zero.

The registered study ctmle-oat-per-arm measured standard errors 8 to 24 percent too small, flat in \(n\), and its cells with the design pinned to the truth were calibrated. tests/diagnostics/x17_generated_design/run.py adds the term with the true \(g_0\) and restores the ratio to 1.03 at \(n\) = 1,500 and 0.98 at \(n\) = 6,000. The applied revert gives the cells. The term needs \(g_0\), which the design exists to avoid, and the influence function of the outcome learner. No source read here gives either for a flexible learner with the targeting step.

What ships against Appendix D. CTMLE refuses targeting_scheme="fold", so the fluctuation is one pooled coefficient on the stacked out-of-fold rows, as Appendix D outlines. Two divergences remain.

divergence	what ships	what Appendix D outlines
the final average	the stacked whole-sample plug-in, because CTMLE refuses cv_evaluation=True	the \((1/V)\sum_v\) fold average. With fixed \(V\), near-balanced unweighted folds and bounded predictions, the difference is \(O(V/n)\)
the fluctuation dimension	a joint fluctuation with one column for each arm, from which the means, ATE, RR and OR follow	one signed coefficient for the binary ATE

Why the nonparametric shared design is not a natural extension. It fits one shared multinomial mechanism on K estimated columns and uses a K-column joint fluctuation. Cramér–Wold turns proved scalar joint expansions into a vector limit. It does not prove those expansions, their remainders, or the covariance that the shared learned mechanism induces. The cross-fitted default is further outside Theorem 1, because Appendix D only outlines its proof.

Sources read, and why none closes F19.

source	what it lacks
archived ctmle3 and the drtmle adapt_g option	each is implementation provenance and reports the ordinary curve. Neither is an inference theorem
DOPE, Theorem 4.3 and Proposition 4.4	it proves inference for a data-adaptive target conditional on a representation learned on an independent sample. A fixed target can need a further delta-method variance. Its appendix leaves the dependent fold-oracle proof open
outcome-adapted AutoDML	a sample-split result, and no result for the cross-fitted construction
Escanciano and Pérez-Izquierdo (2023)	second-step orthogonality removes the indirect first-step effect. The direct effect of learning the generated regressor remains
Zhang, Shao, Yu and Wang (2018); Ma, Zhu, Zhang, Tsai and Carroll (2019), abstracts only	estimated dimension reduction can change the variance or keep efficiency. Neither has a targeting step or a shared multinomial mechanism
Schnitzer, Talbot, Liu et al. (2026), Statistics in Medicine 45(1-2):e70316, abstract only	it selects covariates for a longitudinal treatment model, and fits no mechanism on estimated outcome predictions

Open items. A result states a verdict on each one.

open item	what a result must settle
the per-arm generated-design term	an analogue of \(c^\top \mathrm{IF}_\beta\) for a flexible outcome learner, or an estimator of the term that does not need a consistent full mechanism when no other derivation supplies one, or a source that shows the term vanishes under a stated condition. X58 may use a known or consistently estimated full mechanism, and it does not need to settle this item
one shared multinomial	one categorical fit on K estimated columns supplies every arm’s clever covariate, so an inconsistent column for one arm enters every other arm’s mechanism
vector target and simultaneous inference	the joint covariance and the simultaneous critical value, not the per-arm variance alone
uniformity, for both designs	each estimator is superefficient by design, so a pointwise limit law does not give locally uniform coverage. A pointwise claim under stated regularity conditions, such as the X58 claim, does not need a uniformity result. It states that it is pointwise
transport of the shared design beyond the source law	missing outcomes need the response-mechanism expansion. Fixed weights need a weighted empirical-law result, and estimated weights a first-stage contribution. Clusters and strata need dependence- and stratum-specific expansions. Repeats need the median and split-dispersion aggregation

Acceptance.

• A result covers the exact cross-fitted multi-arm construction, and it separates a fixed target from a target conditional on the learned design.

• For the per-arm design, the revert cells of ctmle-oat-per-arm pass their declared bands under a fresh declaration. The support predicate per_arm_parametric_support replaced the global per-arm flag, and it admits the validated configurations only. X58 part (a) shipped its first scope.

• It establishes whether the current curve suffices or an added representation contribution is needed.

• It covers the requested joint means or contrasts and their covariance. It states the remainder, the nuisance-rate conditions, and whether its claim is pointwise or locally uniform.

• A new contribution propagates through pointwise and simultaneous inference.

• The evidence needs a fixed-design reduction, a generated-design comparison, and registered coverage for every claimed treatment and target dimension.

• A contraction of the generated-design pair needs a two-sided equivalence margin or a declared sample-size ladder. A deliberately invalid design can serve as a negative control, and the learned design cannot.

The registered evidence is in the point-treatment and multi-arm studies. The point-treatment generated-design pair passes its own calibration bands. The multi-arm pair passes its coverage band, and both of its standard-error intervals cross the 1.07 upper bound. No result there identifies a first-order term.

F21. Other missing-outcome CV-TMLE variants

X53 holds the TMLE variants: fold targeting, the median over a fixed number of splits, a cross-fitted missing treatment, the off-contract axes, and the four stacked follow-ups. This item keeps the cross-fitted DRTMLE compositions.

kept claim	kind	missing argument
a cross-fitted DRTMLE with delta= or a missing treatment	asymptotic	the package’s own argument for the cross-fitted DR-TMLE leaves the pooled reduced cross-fit term [B] open (DR-TMLE targeting). No cross-fitting lemma reaches it
reduced_crossfit="nested" on the composite	asymptotic	the nested construction removes term [B], so it is the candidate route for a later reading. The cross-fit refusal comes first today, so no request reaches the nested composite
reduced_crossfit="nested" on the randomized missing-outcome DRTMLE	asymptotic	the nested construction needs the argument that the composite row lacks. No read source gives it for the randomized missing-outcome route. DRTMLE refuses it before any learner

A cross-fitted DRTMLE fit with missing outcomes refuses before any learner, and its message names this item. A C-TMLE selector fit takes working_mechanism_plugin, which F18 holds. Every strategy="oat" fit takes generated_design_plugin, which F19 holds.

F22. Grouped cross-fitting beyond point-treatment TMLE

The package draws whole-cluster outer folds for the ordinary cross-fitted point-treatment TMLE, DR-TMLE and longitudinal TMLE. The C-TMLE selector and outcome-adaptive paths refuse id= at every cross_fit setting. CTMLE(strategy="derivative") admits id= with the TMLE clustered result. X51 part (e) holds the clustered point estimates, with a cluster as the unit and whole-cluster folds. The clustered versions of the parametric cells, X58’s cells included, move with X52 part (d). This item keeps every other clustered C-TMLE interval. Its kind is asymptotic.

composition	what ships	what a result must supply
a C-TMLE selector or outcome-adaptive interval with id=	refused at every cross_fit setting (CTMLE._resolve_estimands_for_data)	a split law for the selection folds and the nested selection folds under clustering, and the cluster-robust variance of the candidate the search stops at. F18 and F19 are open for iid rows, so a clustered result needs them first

The other grouped compositions take the cluster as the sampling unit, and the natural-extension verdicts qualify them as natural extensions. The cross-fitted interval at unequal cluster sizes and the \(t\) reference at few clusters ship (clusters), and F28 holds their finite-sample limits. Cross-fitted longitudinal TMLE with id= ships with whole-cluster folds (longitudinal clusters).

The grouped point-treatment split is supported for the partition alone. Wang, Park, Small and Li (2024), Section 4.2 and Theorem 4(b), prove a cross-fitted result under a random, roughly equal partition of the clusters. Their estimator is AIPW-type with a cluster-level treatment. The rest is the package’s own estimating-equation argument, which the fold and outcome-scale rules state with its four conditions: independent clusters, equal cluster sizes, no interference, and the usual remainder rates. The registered clustered point-treatment CV-TMLE study is its only empirical witness.

The source audit found related work. Grouped folds and clustered cross-fitting gives every source the audit read, with the version whose locators it used.

source	what it covers
Nugent et al. (2024)	grouped folds and aggregated cluster influence curves in partially clustered trials
Balkus, Laith and Hejazi (2026)	splitting correlated units can still remove an empirical-process term under their conditions
Karim (2026)	point-treatment survey TMLE
the JSS ltmle article	longitudinal software
Zeileis, Köll and Graham (2020)	clustered sandwich covariances for regression models

None supplies a split law or a variance for the clustered C-TMLE search.

F5. Other refused C-TMLE and DR-TMLE compositions

X50 holds the DR-TMLE regimes, discrete-arm MSMs, the natural course with missing outcomes, evaluation= on the composite, the omitted-variable bound, and estimated weights with a guard. X51 holds the C-TMLE point estimates for the natural course, regimes, discrete-arm MSMs, a selector missing treatment, clusters, and the omitted-variable bound. X62 holds the other compositions that a natural extension carries. This item keeps the compositions below.

kept claim	kind	missing argument
C-TMLE ATT and ATC	regularity	the clever covariate and the treated covariate law read \(g\), so the target is not a function of \(Q\) alone. van der Laan and Gruber (2009), WP 246, Theorem 2, needs that form
C-TMLE incremental, modified treatment policies and the risk-ratio tilt	regularity	each candidate \(g\) of the collaborative search defines a different parameter, so collaborative consistency fails. The risk-ratio tilt is the lmtp ipsi rule, a known two-point randomizer on the natural value, so it joins the modified treatment policies
C-TMLE controlled direct effect	regularity	a collaborative path over two mechanisms. Schnitzer, Sango, Ferreira Guerra and van der Laan (2020), Biometrics 76(1):145-157, may give a published point method. The review read its abstract only, and its first-hand read is pending
C-TMLE on a continuous dose	regularity	a collaborative candidate sequence of conditional density estimators. No read source derives one
C-TMLE on a longitudinal functional	regularity	a sequential collaborative score. No read source derives one
DR-TMLE ATT, ATC, modified treatment policies, the risk-ratio tilt and incremental	asymptotic	Benkeser, Carone, van der Laan and Gilbert (2017), PMC5793673, Section 4, name other parameters as future work. Díaz et al., arXiv:2006.01366v4, Theorem 2, assumes that the regime does not depend on \(P\)
DR-TMLE controlled direct effect and longitudinal functionals	asymptotic	Benkeser et al. (2017), Section 1, name interventions at several time points as future work
DR-TMLE on a continuous dose, with its evaluation companion and its nested construction	asymptotic	reduced regressions that condition on a conditional density in place of an arm probability. No read source derives them
DR-TMLE combined with C-TMLE	asymptotic	a reduced regression conditions on the collaborative \(\hat g\). The reduced-dimension correction needs \(\hat g \to g_0\), which C-TMLE does not give
a partial guard on the randomized missing-outcome DR-TMLE	asymptotic	the shipped algorithm targets the treatment, observation and outcome correction blocks jointly. No read source gives a result for a subset of the three blocks
DR-TMLE with targeting_scheme="fold" or cv_evaluation=True	asymptotic	each fold’s reduced regressions and alternation, and a corrected curve under fold-wise evaluation. No read source gives a fold-evaluated DR-TMLE, as F27 records for the learned-rule value

Ordinary-TMLE implementations do not establish the C-TMLE or DR-TMLE corrections for these compositions. Each pre-fit refusal names this item and an alternative that ships, in most cases a plain TMLE.

F27. Learned-policy value outside the published conditions

The learned-rule contract refuses each request below before any learner, except the exceptional-law row. The boundary study measures the exceptional-law row and the weak_blip row. F27 owns every red cell of the boundary study. X11 parts (c) and (i) to (o) hold the compositions that moved.

kept claim	kind	missing argument
an interval at an exceptional law, where the limiting-rule condition C3 of that contract fails	adaptive-optimum inference	a CV-TMLE interval for the fold-average target without a limiting rule. van der Laan and Luedtke (2015), Theorem 6, and Hubbard et al. (2016), Theorem 1, both need a limit curve. Luedtke and van der Laan (2016), Annals of Statistics, Section 4.2, name inverse weighting by the standard deviation and a central limit theorem for triangular arrays. Section 5 applies them to the optimal value. Fava (2026), arXiv:2610.02944v1, covers a known-propensity IPW score only
the full-refit bootstrap	asymptotic	each resample relearns the rules, so each draw has a different target. No read source gives the bootstrap law of a data-adaptive target
a continuous treatment	regularity	a deterministic dose rule gives the value of fixed doses, which is not pathwise differentiable
a fold-evaluated DRTMLE learned rule	asymptotic	no read source gives a fold-evaluated DR-TMLE. DRTMLE refuses cv_evaluation=True for that reason
CTMLE with learned_rule=	adaptive-optimum inference	the selector and outcome-adaptive paths have no interval for any target, as F18 and F19 record
missing outcomes or a missing treatment with learned_rule=	asymptotic	van der Laan and Luedtke (2015) treat complete outcomes, and no read source gives a cross-fitted learned-rule fit with missing outcomes or a missing treatment. The missingness tilt is unreachable for the same reason. The missing-treatment refusal (composite.py) cites this row
an E-value for a learned-rule contrast	regularity	no E-value of a regime contrast ships (evalue.py, the arm-contrast check). A regime contrast is not a contrast of two exposure levels, so the bound needs its own mapping

The weak_blip row has no missing result. That law is within C3, and Theorem 6 of van der Laan and Luedtke (2015) covers it. A red cell there is a finite-sample limit at n = 2,000, and F27 holds it as the owner of the reporting study.

F28. Finite-sample limits of clustered intervals

A clustered TMLE or DRTMLE fit reports a Student \(t\) interval with \(J-2\) degrees of freedom when it reads 10 to 39 clusters with positive weight mass, and an LTMLE fit, in sample or cross-fitted, when it reads 20 to 39 (clusters). From 3 clusters up to that floor, in the fit or in one reported baseline stratum, the fit takes the "few_cluster_plugin" status and shows its interval under the experimental label. Below 3 clusters it takes "no_cluster_variance_plugin" and withholds the interval. Each floor is the smallest count the registered few-cluster study measures for that fit.

kept claim	kind	missing argument
an interval below 4 clusters	arbitrary dependence	a supported construction for a fixed number of dependent units. Below 4 clusters the reference has fewer than 2 degrees of freedom, and at 2 clusters or fewer no independent-cluster argument applies

X54 parts (a) to (h) hold the registered measurements from 3 clusters up to each floor, and the other small-sample work. The cluster-as-unit theory is the same at 4 clusters as at 10, so that work needs evidence and not a theorem. F28 stays the owner id of the clustered red cells, and X54 is the work that closes them.

F29. The ctmleGlmnet type-2 path

R ctmle 0.1.2 accepts ctmletype = 2 in ctmleGlmnet. No published source defines it. Its documentation reads “See more details in !!!” (R/ctmle_glmnet.R, lines 11 and 12), and Ju, Wyss et al. (2019) describe only C-TMLE1 and C-TMLE0. The code is not consistent with itself.

place	what it does
construction (R/functions_glmnet.R, lines 151 to 155)	the finite difference reads the previous remaining penalty, or the current penalty plus an absolute 0.005
evaluation (R/functions_glmnet.R, lines 36 to 40)	the finite difference reads the previous grid penalty
ctmleGeneral type 2 (R/functions_general.R, lines 34 to 36)	errors, because eps_try is undefined

F29 reopens when a published algorithm defines the type-2 sequence and its fluctuation.

F31. Inference at a boundary node estimate

A longitudinal fit reads a node regression whose fitted rows all hold 0, or all hold 1, as that value (a node with no event). The point estimate is the maximum-likelihood value, and survtmle reads such a node the same way. The node’s term of the influence curve is then identically zero, although the true hazard there can be positive. So the plug-in standard error leaves that node’s variance out.

X54 part (i) holds the interval at a fixed law. There a zero-event node has exponentially small probability, so the shipped theorem covers an interval that differs from the ordinary one only on that event.

kept claim	kind	missing argument
an interval in the rare-event local regime, where the node hazard \(h_n\) tends to 0	asymptotic	a limit theorem for a TMLE parameter whose node hazard shrinks with \(n\). Boundary theory, such as Andrews (1997), assumes the truth on the boundary. The review read its abstract only

F32. Fold policies that read the treatment or the outcome

stratify_folds can draw the outer folds inside strata of the treatment or the outcome. learners/crossfit.py refuses that split before any learner. The fold and outcome-scale rules give the audit. Zheng and van der Laan (2011), WP 273, draw the split vector uniformly over a finite support. Polley (2010) proves the Super Learner oracle result for folds drawn independently of the learning sample.

kept claim	kind	missing argument
outer folds stratified on the treatment or the outcome	asymptotic	a result that keeps the cross-fitted remainder argument when the partition is a function of \(A\) or \(Y\). Each read result draws the split independently of the data

F33. Other intervention and design compositions

Each request below is well posed, and each one refuses before any learner. X63 and X64 hold the declarations that a natural extension carries. This item keeps the compositions that need an argument of a new kind.

kept claim	kind	missing argument
the composite missing-treatment indicator with a controlled direct effect	identification	a stated condition that ties \(Z\) to the recording of the treatment. No source read here states one. The shared preflight in estimators/composite.py refuses the fit
an IPSI plan with a modified-treatment-policy node or a risk-ratio-tilt node	regularity	a density ratio at each modified-policy or risk-ratio-tilt node inside the cross-fitted IPSI estimator, beside the mechanism term of each odds-tilt node. No read source derives the mixed plan. longitudinal/regimen.py refuses it. X57 holds the point-treatment joint axes
an MSM projection weight from a learned mechanism	regularity	the weight is a functional of \(P\), so the curve needs the pathwise derivative through the learned mechanism. No read source gives that term for the shipped projection. msm.py refuses it. X64 part (d) holds finite-dimensional weights and designs
automatic selection of the cumulative bound for LTMLE	adaptive-optimum inference	inference after a data-adaptive bound selector. utils/bounds.py refuses a named selector. The fixed heuristic (0.01, 1.0) ships as the default

F34. E-values beyond the total-population arm contrast

The shipped E-value converts a risk ratio of two exposure levels in the total population. Ding and VanderWeele (2016), Sensitivity analysis without assumptions, give its bounding factor. X49 applies that bound to each arm of a controlled direct effect. The requests below refuse before any computation.

kept claim	kind	missing argument
the ATT and ATC E-value on a binomial outcome	identification	a cited bound for the causal risk ratio among the treated or the controls, with its reading of the strengths. Among the treated only the control-arm counterfactual is confounded, so the total-population factor does not carry over by name. No source read here states that bound. sensitivity/evalue.py refuses the request
the E-value of a regime, policy or incremental contrast, and the derived risk ratio off the arm axis	identification	a regime contrast is not a contrast of two exposure levels, so the bound needs its own mapping, as F27 records for a learned rule. The derived ratio off the arm axis has no consumer until that mapping exists. sensitivity/_derived.py refuses it

F35. Inference for sequential baselines with data-adaptive nuisances

SequentialGComputation and SequentialIPW report an interval only when every regression they read is a GLM. The interval is then the stacked estimating equation of the parametric fits. With another learner the estimator solves no efficient influence-curve equation. Its first-order bias is then of the order of the learner’s error.

kept claim	kind	missing argument
an interval for sequential g-computation with a data-adaptive outcome learner	asymptotic	an asymptotic-linearity theorem for the iterated conditional expectation plug-in over several time points, such as an undersmoothing result. No source read here derives one
an interval for longitudinal IPW with a data-adaptive mechanism learner	asymptotic	the same result for the cumulative weights. Ertefaie, Hejazi and van der Laan (2023), Section 3, Theorem 1, cover IPW with an undersmoothed highly adaptive lasso propensity at a single time point only
a cross-fitted baseline, n_folds above 1	asymptotic	the same result for cross-fitted nuisances. Cross-fitting does not remove the first-order bias of a plug-in or IPW estimate, so the in-sample result does not carry over

F36. Locally efficient g-estimation of the structural nested mean model

StructuralNestedMean solves the unweighted g-estimating equation. Its instrument is the residual treatment \(\tilde Z_{t,t}\). The semiparametric efficient estimator of a structural nested mean model weights that instrument by the conditional variance of the outcome residual. The shipped estimator is not that one, and no result read for this item ranks its variance against the variance of LTMLE. The weighted instrument also needs a nuisance for that variance.

kept claim	kind	missing argument
an interval for the blips from the variance-weighted g-estimator, with a cross-fitted variance nuisance	efficiency	the efficient influence function of the linear structural nested mean model, and a limit theorem for the cross-fitted weighted estimator. No source read for this item states either

Reading a gap correctly

Not every absence is missing package functionality. The five reason codes in How to read a refusal separate an implementation_gap and an inference_gap from an invalid_declaration, a different_estimand, and an api_redirection. Only the first two belong on this roadmap. Each implementation_gap refusal names the item that tracks it. tests/unit/test_refusal_codes.py checks each one in the source and in each module-level record.