Longitudinal incremental interventions

This study validates IPSI in cleverly.longitudinal. IPSI is the one-step estimator of Kennedy (2019), Algorithm 1, for incremental propensity-score interventions over time. The incremental interventions over time section states the estimator, its conditions and its exact-law evidence.

The evidence label is Python property evidence, with comparator runs pending. The study declares R npcausal 0.1.0 at commit 56a5ac11 as its comparator. The comparator runs have not registered, so this page publishes no paired verdict. Comparator runs pending states the rule. The dropout study measures the same estimator under dropout, survival outcomes, weights and clusters.

What was compared

scenario	law and plans	folds
ipsi_folds_2	law A of tests/discrete_law_longitudinal_incremental.py: a binary baseline covariate, a binary treatment, a binary L2 and L3, and a continuous end-of-study outcome over three nodes. Three plans tilt every node by 0.5, 1 (the natural course) and 2	two
ipsi_folds_5	the same law and plans	five

Each scenario reports five estimands: the three plan means and the two contrasts with the natural course. The one-fold fit is not a primary scenario. npcausal 0.1.0 cannot fit one fold, because its training rows are empty at nsplits = 1. The one-fold fit is the calibration label contrast_x2_in_sample instead.

setting	cleverly	R npcausal (declared, pending)
datasets	1,000 samples of 96,000 rows per scenario	the identical rows
nuisance fits	saturated cell means (CellMeans) at every slot	SL.cellmeans in tests/canonical/npcausal_ipsi_adapter.R
folds	the Python fold assignment	the same assignment, which replaces the npcausal fold draw
treatment model	cell means by node and history	one model over every (id, time) row, with the time block and the history cell as design
intervals	pointwise 95% Wald from the influence curve	the same, from its influence values (ifvals), with no factor between the two standard errors

With equal cell partitions and equal fallbacks, the two recursions are the same function of the sample. The pairing gates G1 and G2 in tests/canonical/npcausal_longitudinal_incremental/gates.py test this before the study.

Each gate requires agreement below PAIRING_GATE (1e-10) on the estimate, every influence value and the standard error. The committed gates.csv holds 42 plan rows. All 42 pass, and the largest gap is 2.5e-12, on an influence value. The gates are pre-declaration checks. They are not paired verdicts.

Accuracy against known truth

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
three-node law with a continuous outcome, two folds	ate_regimen[odds x0.5 vs natural course]	difference in mean outcome between the plans “multiply the treatment odds by 0.5” against “leave the observed treatment mechanism unchanged”	cleverly IPSI, one-step over time	-0.000593 to -0.000138	0.9470	1.0251	pass
three-node law with a continuous outcome, two folds	ate_regimen[odds x2 vs natural course]	difference in mean outcome between the plans “multiply the treatment odds by two” against “leave the observed treatment mechanism unchanged”	cleverly IPSI, one-step over time	0.000137 to 0.000632	0.9440	0.9934	pass
three-node law with a continuous outcome, two folds	ey_regimen[natural course]	mean outcome under the plan leave the observed treatment mechanism unchanged	cleverly IPSI, one-step over time	-0.000693 to 0.000554	0.9490	1.0030	pass
three-node law with a continuous outcome, two folds	ey_regimen[odds x0.5]	mean outcome under the plan multiply the treatment odds by 0.5	cleverly IPSI, one-step over time	-0.0010 to 0.000176	0.9490	1.0012	pass
three-node law with a continuous outcome, two folds	ey_regimen[odds x2]	mean outcome under the plan multiply the treatment odds by two	cleverly IPSI, one-step over time	-0.000297 to 0.000928	0.9530	1.0119	pass
three-node law with a continuous outcome, five folds	ate_regimen[odds x0.5 vs natural course]	difference in mean outcome between the plans “multiply the treatment odds by 0.5” against “leave the observed treatment mechanism unchanged”	cleverly IPSI, one-step over time	-0.000533 to -0.000063	0.9600	0.9935	pass
three-node law with a continuous outcome, five folds	ate_regimen[odds x2 vs natural course]	difference in mean outcome between the plans “multiply the treatment odds by two” against “leave the observed treatment mechanism unchanged”	cleverly IPSI, one-step over time	-0.000010 to 0.000469	0.9530	1.0282	pass
three-node law with a continuous outcome, five folds	ey_regimen[natural course]	mean outcome under the plan leave the observed treatment mechanism unchanged	cleverly IPSI, one-step over time	-0.000348 to 0.000903	0.9350	1.0001	pass
three-node law with a continuous outcome, five folds	ey_regimen[odds x0.5]	mean outcome under the plan multiply the treatment odds by 0.5	cleverly IPSI, one-step over time	-0.000629 to 0.000589	0.9450	1.0041	pass
three-node law with a continuous outcome, five folds	ey_regimen[odds x2]	mean outcome under the plan multiply the treatment odds by two	cleverly IPSI, one-step over time	-0.000122 to 0.0011	0.9480	0.9859	pass

Agreement with the canonical implementation

Python property evidence, with comparator runs pending. This section holds no paired table, because the comparator study has not run. equivalence.csv records no row.

item	state
comparator	R npcausal 0.1.0 ipsi() at commit 56a5ac11, on a digest-pinned R 4.5.2 image
reason pending	the npcausal R phase runs on the local study queue and registers in a later change
paired cell of the grid	0/0 external comparisons, with the pending label
declared margins	the paired margins in the measured table below. No cell reads them yet
what the later run adds	five paired tests for each scenario, read against the default Margins()

The owner’s rule applies: a method merges on its Python evidence, and the comparator study follows (Theory and comparators). When the run registers, the paired block and the paired counts replace this section.

Theory properties

property	cell	role	what was tested	what must hold	measured	result
interval_calibration	contrast_x2__correctly_specified	positive	odds-x2 against the natural course, three-node law: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9327 to 0.9546, SE ratio 0.9489 to 1.0161, empirical efficiency ratio 0.9848 to 1.0545, reported efficiency ratio 1.0005 to 1.0009	pass
interval_calibration	contrast_x2__noise_control	control	odds-x2 against the natural course, three-node law: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8120 to 0.8476, SE ratio 0.6742 to 0.7210, empirical efficiency ratio 1.3880 to 1.4842, reported efficiency ratio 1.0005 to 1.0009	pass
interval_calibration	contrast_x2__shrunken_se_control	control	odds-x2 against the natural course, three-node law: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8002 to 0.8368, SE ratio 0.6639 to 0.7111, empirical efficiency ratio 0.9851 to 1.0550, reported efficiency ratio 0.7003 to 0.7006	pass
interval_calibration	contrast_x2_in_sample__correctly_specified	positive	odds-x2 against the natural course, one fold: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9374 to 0.9585, SE ratio 0.9492 to 1.0152, empirical efficiency ratio 0.9851 to 1.0535, reported efficiency ratio 0.9999 to 1.0003	pass
interval_calibration	contrast_x2_in_sample__noise_control	control	odds-x2 against the natural course, one fold: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8207 to 0.8556, SE ratio 0.6925 to 0.7391, empirical efficiency ratio 1.3532 to 1.4442, reported efficiency ratio 0.9999 to 1.0004	pass
interval_calibration	contrast_x2_in_sample__shrunken_se_control	control	odds-x2 against the natural course, one fold: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8006 to 0.8371, SE ratio 0.6646 to 0.7111, empirical efficiency ratio 0.9845 to 1.0533, reported efficiency ratio 0.6999 to 0.7002	pass
interval_calibration	known_x2__correctly_specified	positive	odds-x2 mean with the true treatment probabilities declared: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9385 to 0.9594, SE ratio 0.9785 to 1.0509, empirical efficiency ratio 0.9519 to 1.0223, reported efficiency ratio 1.0002 to 1.0006	pass
interval_calibration	known_x2__noise_control	control	odds-x2 mean with the true treatment probabilities declared: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8307 to 0.8648, SE ratio 0.7020 to 0.7507, empirical efficiency ratio 1.3328 to 1.4254, reported efficiency ratio 1.0002 to 1.0007	pass
interval_calibration	known_x2__shrunken_se_control	control	odds-x2 mean with the true treatment probabilities declared: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8224 to 0.8572, SE ratio 0.6858 to 0.7349, empirical efficiency ratio 0.9529 to 1.0211, reported efficiency ratio 0.7001 to 0.7005	pass
interval_calibration	mean_x2__correctly_specified	positive	odds-x2 mean at every node, three-node law: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9392 to 0.9600, SE ratio 0.9834 to 1.0476, empirical efficiency ratio 0.9547 to 1.0170, reported efficiency ratio 1.0001 to 1.0004	pass
interval_calibration	mean_x2__noise_control	control	odds-x2 mean at every node, three-node law: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8144 to 0.8498, SE ratio 0.6815 to 0.7267, empirical efficiency ratio 1.3763 to 1.4677, reported efficiency ratio 1.0001 to 1.0004	pass
interval_calibration	mean_x2__shrunken_se_control	control	odds-x2 mean at every node, three-node law: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8189 to 0.8540, SE ratio 0.6869 to 0.7333, empirical efficiency ratio 0.9548 to 1.0193, reported efficiency ratio 0.7001 to 0.7003	pass
interval_calibration	no_positivity__correctly_specified	positive	odds-x2 contrast on a law with propensities of exactly 0 and 1: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9345 to 0.9561, SE ratio 0.9653 to 1.0331, empirical efficiency ratio 0.9680 to 1.0361, reported efficiency ratio 0.9997 to 1.0004	pass
interval_calibration	no_positivity__noise_control	control	odds-x2 contrast on a law with propensities of exactly 0 and 1: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8162 to 0.8514, SE ratio 0.6938 to 0.7393, empirical efficiency ratio 1.3527 to 1.4411, reported efficiency ratio 0.9997 to 1.0004	pass
interval_calibration	no_positivity__shrunken_se_control	control	odds-x2 contrast on a law with propensities of exactly 0 and 1: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8127 to 0.8483, SE ratio 0.6759 to 0.7234, empirical efficiency ratio 0.9676 to 1.0358, reported efficiency ratio 0.6998 to 0.7003	pass
interval_calibration	per_node__correctly_specified	positive	odds multipliers 2, 0.5 and 1.5 at the three nodes: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9381 to 0.9591, SE ratio 0.9777 to 1.0445, empirical efficiency ratio 0.9575 to 1.0229, reported efficiency ratio 1.0000 to 1.0003	pass
interval_calibration	per_node__noise_control	control	odds multipliers 2, 0.5 and 1.5 at the three nodes: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8179 to 0.8530, SE ratio 0.6929 to 0.7402, empirical efficiency ratio 1.3513 to 1.4435, reported efficiency ratio 1.0000 to 1.0003	pass
interval_calibration	per_node__shrunken_se_control	control	odds multipliers 2, 0.5 and 1.5 at the three nodes: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8207 to 0.8556, SE ratio 0.6852 to 0.7323, empirical efficiency ratio 0.9561 to 1.0217, reported efficiency ratio 0.7000 to 0.7002	pass
interval_calibration	tilt_then_static__correctly_specified	positive	odds-x2 at nodes 1 and 2, then arm 1 at node 3: both nuisances are correctly specified with an independently computed efficiency bound	SE ratio and coverage intervals both inside their calibration bands, with both efficiency-ratio intervals inside their bands	coverage 0.9436 to 0.9636, SE ratio 0.9811 to 1.0474, empirical efficiency ratio 0.9559 to 1.0207, reported efficiency ratio 1.0012 to 1.0016	pass
interval_calibration	tilt_then_static__noise_control	control	odds-x2 at nodes 1 and 2, then arm 1 at node 3: one efficiency-bound unit of independent noise is added to each estimate	the empirical efficiency ratio must rise above the band	coverage 0.8148 to 0.8502, SE ratio 0.6759 to 0.7214, empirical efficiency ratio 1.3881 to 1.4817, reported efficiency ratio 1.0012 to 1.0016	pass
interval_calibration	tilt_then_static__shrunken_se_control	control	odds-x2 at nodes 1 and 2, then arm 1 at node 3: the reported standard errors are multiplied by a declared factor below one	the SE-ratio interval must fall below the calibration band	coverage 0.8193 to 0.8543, SE ratio 0.6866 to 0.7349, empirical efficiency ratio 0.9538 to 1.0211, reported efficiency ratio 0.7008 to 0.7011	pass
mechanism_term_necessity	contrast_x2__full_eif	positive	odds-x2 against the natural course, three-node law: the reported standard error from the full influence curve	the SE-ratio interval inside the efficiency-ratio band	SE ratio 0.9619 to 1.0285	pass
mechanism_term_necessity	contrast_x2__mechanism_term_dropped	control	odds-x2 against the natural course, three-node law: the same estimates with the treatment-mechanism term, on the outcome’s own scale, removed from the curve	the SE-ratio interval must fall below the calibration band	SE ratio 0.7524 to 0.8025	pass
power	contrast_x1_5__alternative	positive	odds-x1.5 against the natural course, small arm effects: the same test applied to a law with a real effect	rejection lower bound clears the minimum power	rejection 0.8900, 0.8708 to 0.9073	pass
root_n_and_efficiency	contrast_x2__n_24000	control	odds-x2 against the natural course, three-node law: bias, coverage and SE calibration at n = 24,000	coverage interval lies below nominal or clears the declared floor	bias 0.000729, coverage 0.9389 to 0.9726, SE ratio 1.0254	pass
root_n_and_efficiency	contrast_x2__n_64000	positive	odds-x2 against the natural course, three-node law: bias, coverage and SE calibration at n = 64,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000343, coverage 0.9295 to 0.9661, SE ratio 1.0070	pass
root_n_and_efficiency	contrast_x2__n_96000	positive	odds-x2 against the natural course, three-node law: bias, coverage and SE calibration at n = 96,000	bias inside the margin, coverage clears the floor, SE ratio inside the sanity band	bias 0.000094, coverage 0.9283 to 0.9652, SE ratio 0.9911	pass
root_n_rate	contrast_x2__empirical_sd	positive	odds-x2 against the natural course, three-node law: log empirical spread of the estimates regressed on log n across three sizes	slope interval inside the root-n band and excluding -1/4	slope -0.5333 to -0.4210	pass
root_n_rate	contrast_x2__reported_se	positive	odds-x2 against the natural course, three-node law: the same regression applied to the mean reported standard error	slope interval inside the root-n band and excluding -1/4	slope -0.5009 to -0.5000	pass
simultaneous_coverage	nine_tilts__pointwise_joint_control	control	nine odds multipliers from 0.25 to 4, their means and eight contrasts: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.7651 to 0.8125	pass
simultaneous_coverage	nine_tilts__simultaneous_band	positive	nine odds multipliers from 0.25 to 4, their means and eight contrasts: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9239 to 0.9520	pass
single_robustness	contrast_x2__mechanism_constant	diagnostic	odds-x2 against the natural course, three-node law: constant treatment mechanism and cell-mean outcome regressions, beside the exact-law limit	reported only	bias 0.1252 to 0.1261, margin 0.0013, coverage 0.0000	reported
single_robustness	contrast_x2__mechanism_correct__n_48000	positive	odds-x2 against the natural course, three-node law: cell-mean treatment mechanism and linear outcome regressions, at n = 48,000	bias inside the margin at n = 48,000 and at n = 96,000	bias -0.000083 to 0.000610, margin 0.0011, coverage 0.9530	pass
single_robustness	contrast_x2__mechanism_correct__n_96000	positive	odds-x2 against the natural course, three-node law: cell-mean treatment mechanism and linear outcome regressions, at n = 96,000	bias inside the margin at n = 48,000 and at n = 96,000	bias 0.000160 to 0.000648, margin 0.000747, coverage 0.9450	pass
targeting_necessity	contrast_x2__one_step	positive	odds-x2 against the natural course, three-node law: the one-step estimate with linear outcome regressions	bias inside the margin	bias -0.000058 to 0.000424, margin 0.000738	pass
targeting_necessity	contrast_x2__plug_in	control	odds-x2 against the natural course, three-node law: the mean of the first-node regression before the correction, on the same fits	bias interval outside the margin	bias -0.0016 to -0.0012, margin 0.000717	pass
type_i_error	contrast_x2__sharp_null	positive	odds-x2 against the natural course, three-node law: a confounded law whose true contrast is exactly zero	one-sided rejection bound stays under the declared type-I ceiling	rejection 0.0505, 0.0387 to 0.0645	pass

Every cell passes, and no property fit failed.

Every property fit uses five folds, saturated cell means at every slot and law A. The table names any other setting. x2 is the plan that doubles the odds of treatment at every node. contrast_x2 is ate_regimen[odds x2 vs natural course]. tests/studies/longitudinal_incremental_properties.py declares every cell.

family	cells and fits	what must hold
interval_calibration	seven labels with three cells each: the correctly specified fit and two derived controls. 3,000 draws at n = 48,000 per label	SE ratio and coverage intervals inside the calibration bands, and both efficiency-ratio intervals inside their band. The shrunken-SE control falls below the band. The noise control rises above the efficiency-ratio band
root_n_and_efficiency	contrast_x2 at n = 24,000 (the control), 64,000 and 96,000. 1,000 draws each	the shared bias, coverage and SE rules. The smallest rung is the control
root_n_rate	two rate rows of contrast_x2, from the ladder above	the slope interval lies inside the root-n band and excludes -1/4
type_i_error	contrast_x2 on law A0, where every tilt has one mean. 2,000 draws at n = 4,000	the one-sided rejection bound stays under the type-I ceiling
power	odds x1.5 vs natural course on law Aw. 2,000 draws at n = 4,000	the rejection lower bound clears the minimum power
simultaneous_coverage	the band over nine tilts on geomspace(0.25, 4, 9), with nine means and eight contrasts, and its pointwise control. 2,000 draws at n = 5,000	the band’s joint coverage interval lies inside the calibration coverage band. The pointwise control’s joint coverage interval lies below the nominal rate
mechanism_term_necessity	contrast_x2 fits on their own draws of law A, with the full curve, and with the mechanism term dropped (the control). 3,000 draws at n = 48,000	the full curve’s SE-ratio interval lies inside the efficiency-ratio band. The control’s interval lies wholly below the calibration band
single_robustness	linear outcome regressions with a correct mechanism, at n = 48,000 and 96,000, and a constant mechanism at n = 48,000 (reported). 1,000 draws each	the two positive cells pass the bias-equivalence rule. The pair tests equivalence at two sizes, not a falling bias. The constant-mechanism cell states no verdict
targeting_necessity	the single_robustness fit at n = 96,000 on its own draws: the one-step estimate, and the plug-in mean of the first-node regression (the control). 1,000 draws	the one-step bias lies inside the margin. The plug-in bias lies outside it, and the plug-in mean sits at least 0.25 one-step standard deviations from the one-step mean

The calibration labels:

label	law, plan and estimand	efficiency bound
mean_x2	A, ey_regimen[odds x2]	exact influence-curve standard deviation
contrast_x2	A, contrast_x2	the same
contrast_x2_in_sample	A, contrast_x2, one fold (Kennedy 2019, Algorithm 2)	the same
known_x2	A, ey_regimen[odds x2], with the law’s own \(\pi_t\) declared, so the curve has no mechanism term	the known-\(\pi\) standard deviation
no_positivity	Ax, exact 0 and 1 propensities and 0.02 cells, contrast_x2 over two nodes	exact influence-curve standard deviation
per_node	A, the multipliers (2, 0.5, 1.5) at the three nodes	the same
tilt_then_static	A, tilts by 2 at nodes 1 and 2, then arm 1 at node 3	the same

The single_robustness cells witness that the estimator is not doubly robust. With a correct mechanism, a linear outcome regression leaves a plug-in that misses the truth, and the weighted residual terms correct it. With a constant mechanism, the estimate carries a bias that the reported cell prints beside its exact-law limit, constant_mechanism_limit in tests/studies/longitudinal_incremental_common.py.

Sizing

The cross-fitted contrasts carry a second-order bias of order 1/n, so their standardized bias falls as \(1/\sqrt n\). The bias rule passes a row only when the 99% interval of its mean error lies inside 0.25 empirical standard deviations. The sizing probe in tests/diagnostics/x19_sizing/ measured the bias at n = 8,000, and each size below projects it.

sizing input	value	source
standardized bias at n = 8,000, five-fold contrasts	0.27	tests/studies/canonical_longitudinal_incremental.py
standardized bias at n = 8,000, two-fold contrasts	0.35	the same
primary n	96,000. The two-fold rows need about 90,000	the same, and tests/unit/test_longitudinal_incremental_design.py
pass probability at the projected bias	at least 0.95 for a primary row and a positive root-n rung. At least 0.90 for a calibration cell	tests/unit/test_longitudinal_incremental_design.py
calibration replications	3,000. At 2,000 an ideal cell passes with probability 0.935, and the seven labels pass jointly with 0.59. At 3,000 each passes with at least 0.99 and the seven jointly with 0.96	tests/studies/longitudinal_incremental_properties.py
calibration n	48,000. The per-cell rule allows 24,000. The larger size cuts the projected bias by a factor of 1.4	the same
robustness sizes	48,000 and 96,000. The probe reads biases of 0.20 at n = 6,000 and 0.11 at 24,000, so 24,000 passes with a probability below 0.95	the same
power cell	2,000 draws. Its rejection rate reads 0.855 at n = 4,000 against an exact-law power of 0.882	the same
band control	the pointwise intervals cover jointly with exact probability 0.811. The control clears the control-power rule at that value plus 0.005	tests/unit/test_longitudinal_incremental_design.py
mechanism-term control	the exact SD ratio is 0.78, below the calibration band	tests/unit/test_longitudinal_incremental_design.py

The fallback-read bias bound holds far below these sizes. The study fixed every size, replication count, margin, law, learner, fold count and seed before any run. After the run, two families moved to their own sample streams, because they reused the fits of another family. The families are mechanism_term_necessity and targeting_necessity. Both were refitted at the declared size and spliced into the committed rows. targeted-refit.json in the study directory records the baseline, the selection, the replacement fits and the identical carried rows. Both families passed before and after the refit.

Red-cell route

event	route, declared before any run
a red primary truth row	blocks the merge and gets a diagnosis
a red paired row, once the comparator registers	gets a diagnosis
a red property cell that reads as a finite-sample limit	is re-registered reporting with an owner row before any re-run
a replication that raises	is never redrawn. The failing cell drops to its owner with its failure count stated as a page limit, and the run repeats without it
any verdict	moves no budget, margin, law, learner, fold count or seed. Controls carry the verdict their family states

Measured values and declared margins

Names beginning margin: are thresholds declared before the run. Names beginning bound: are exact standard errors of the efficient influence curve at the primary n. Everything else is measured from the committed results and checked at the precision printed.

quantity	value	source
replicates	1000	primary replications
n	96000	observations per primary replication
independent_tests_passed	10	truth tests passing
independent_tests_total	10	truth tests reported
property_cells_passed	36	property cells passing
property_cells_total	36	property cells reported
max_standardized_bias	0.1311	largest primary standardized bias
min_coverage	0.9350	lowest primary coverage
margin:confidence_level	0.9900	Monte Carlo confidence level
margin:alpha	0.0500	test size
margin:nominal_coverage	0.9500	nominal interval coverage
margin:bootstrap_replicates	10000	bootstrap replications
margin:standardized_bias	0.2500	standardized-bias margin
margin:coverage_floor	0.9000	primary coverage floor
margin:over_coverage_ceiling	0.9900	descriptive overcoverage threshold
margin:se_ratio_sanity_lower	0.8000	primary SE-ratio lower screen
margin:se_ratio_sanity_upper	1.2000	primary SE-ratio upper screen
margin:calibration_se_ratio_lower	0.9300	calibration SE-ratio lower bound
margin:calibration_se_ratio_upper	1.0700	calibration SE-ratio upper bound
margin:calibration_coverage_lower	0.9200	calibration coverage lower bound
margin:calibration_coverage_upper	0.9800	calibration coverage upper bound
margin:type_i_ceiling	0.1000	type-I upper bound
margin:paired_difference	0.1500	paired similarity margin in pooled SDs. No cell of this study reads it until the comparator runs register
margin:rmse_noninferiority	1.1000	RMSE-ratio noninferiority bound. No cell of this study reads it until the comparator runs register
margin:coverage_noninferiority	-0.0250	coverage-difference noninferiority bound. No cell of this study reads it until the comparator runs register
margin:calibration_noninferiority	0.0500	calibration-excess noninferiority bound. No cell of this study reads it until the comparator runs register
margin:minimum_power	0.8000	minimum power lower bound
margin:root_n_slope	-0.5000	expected root-n slope
margin:root_n_slope_lower	-0.6250	root-n slope lower bound
margin:root_n_slope_upper	-0.3750	root-n slope upper bound
margin:excluded_slope	-0.2500	slower rate the interval must exclude
margin:shrunken_se_factor	0.7000	negative-control SE multiplier
margin:subject_failure_bound	0.0100	declared share of replications a cell may lose to a recordable fitting failure
margin:subject_failures_allowed	10	the same bound, in primary replications
margin:efficiency_ratio_lower	0.9000	exact-EIF ratio lower bound
margin:efficiency_ratio_upper	1.1000	exact-EIF ratio upper bound
margin:targeting_displacement	0.2500	minimum targeting displacement
bound:ate_regimen[odds x0.5 vs natural course]_standard_error	0.0029	exact influence-curve standard error of this estimand at the primary n = 96,000
bound:ate_regimen[odds x2 vs natural course]_standard_error	0.0030	exact influence-curve standard error of this estimand at the primary n = 96,000
bound:ey_regimen[natural course]_standard_error	0.0077	exact influence-curve standard error of this estimand at the primary n = 96,000
bound:ey_regimen[odds x0.5]_standard_error	0.0075	exact influence-curve standard error of this estimand at the primary n = 96,000
bound:ey_regimen[odds x2]_standard_error	0.0076	exact influence-curve standard error of this estimand at the primary n = 96,000

Limits

limit	what it means for use
one law family with three nodes	the evidence covers law A and its variants A0, Aw and Ax, with plans fixed before the run
saturated cell means at every slot	the study does not test a flexible learner. The exact pairing and the sizing rest on cell means
the npcausal comparison is pending	the page publishes no paired verdict. Only the pairing gates G1 and G2 compare the two sides
two and five folds, and one fold in one calibration label	the default of ten folds is not tested
finite-sample bias is sized, not removed	at n = 8,000 the standardized bias reads 0.27 and 0.35. The primary rows pass at the sizes above, and smaller sizes are not claimed
the estimator is not doubly robust	the positive robustness cells hold the mechanism correct. The constant-mechanism cell is reported only
no dropout, survival outcome, competing risk, weight, cluster or working model	the dropout study measures them
the band covers nine declared tilts	the study does not test a band over a continuum of \(\delta\)

Reproduction

tests/canonical/npcausal_longitudinal_incremental/regenerate.py regenerates the study. It runs no reference process while the comparator is pending. The pairing gates need Docker and the cleverly-npcausal:0.1.0-56a5ac1 image. Run them with python -m tests.canonical.npcausal_longitudinal_incremental.gates.