# Ordinary controlled direct-effect TMLE

This study validates ordinary, non-cross-fitted controlled direct-effect TMLE for a binary
intermediate and outcomes missing at random. It compares `cleverly` with R
[`tmle`](https://cran.r-project.org/package=tmle) 2.1.1 on identical samples, with exact outcome,
treatment, intermediate, and observation nuisance predictions supplied to both implementations.
Each replicate draws one sample from a single observed stochastic law. Both intervention levels
use that sample. The controlled effect is negative at level zero and positive at level one.

The comparison reports the two treatment-specific means, ATE, risk ratio, and odds ratio at each
fixed intermediate level, with pointwise 95% Wald intervals. Ratios are assessed on their log
inference scales.

## Accuracy against known truth

<!-- generated: accuracy -->
| law | estimand | what was tested | implementation | bias (99% interval) | coverage | SE ratio | result |
| --- | --- | --- | --- | --- | --- | --- | --- |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `ate` | average treatment effect | `cleverly` controlled direct-effect TMLE | -0.0034 to 0.0014 | 0.9350 | 0.9726 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `ate` | average treatment effect | R `tmle` controlled direct-effect path | -0.0034 to 0.0014 | 0.9350 | 0.9726 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `ey0` | counterfactual mean under no treatment | `cleverly` controlled direct-effect TMLE | -0.000657 to 0.0032 | 0.9216 | 0.9694 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `ey0` | counterfactual mean under no treatment | R `tmle` controlled direct-effect path | -0.000657 to 0.0032 | 0.9216 | 0.9694 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `ey1` | counterfactual mean under treatment | `cleverly` controlled direct-effect TMLE | -0.0011 to 0.0017 | 0.9519 | 1.0125 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `ey1` | counterfactual mean under treatment | R `tmle` controlled direct-effect path | -0.0011 to 0.0017 | 0.9519 | 1.0125 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `or` | marginal odds ratio, reported on the log scale | `cleverly` controlled direct-effect TMLE | -0.0305 to -0.0061 | 0.9331 | 0.9629 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `or` | marginal odds ratio, reported on the log scale | R `tmle` controlled direct-effect path | -0.0305 to -0.0061 | 0.9331 | 0.9629 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `rr` | marginal risk ratio, reported on the log scale | `cleverly` controlled direct-effect TMLE | -0.0046 to 0.0027 | 0.9428 | 0.9802 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `rr` | marginal risk ratio, reported on the log scale | R `tmle` controlled direct-effect path | -0.0046 to 0.0027 | 0.9428 | 0.9802 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `ate` | average treatment effect | `cleverly` controlled direct-effect TMLE | -0.0022 to 0.0021 | 0.9397 | 0.9795 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `ate` | average treatment effect | R `tmle` controlled direct-effect path | -0.0022 to 0.0021 | 0.9397 | 0.9795 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `ey0` | counterfactual mean under no treatment | `cleverly` controlled direct-effect TMLE | -0.0014 to 0.0012 | 0.9419 | 0.9906 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `ey0` | counterfactual mean under no treatment | R `tmle` controlled direct-effect path | -0.0014 to 0.0012 | 0.9419 | 0.9906 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `ey1` | counterfactual mean under treatment | `cleverly` controlled direct-effect TMLE | -0.0018 to 0.0015 | 0.9272 | 0.9779 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `ey1` | counterfactual mean under treatment | R `tmle` controlled direct-effect path | -0.0018 to 0.0015 | 0.9272 | 0.9779 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `or` | marginal odds ratio, reported on the log scale | `cleverly` controlled direct-effect TMLE | -0.0032 to 0.0155 | 0.9409 | 0.9797 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `or` | marginal odds ratio, reported on the log scale | R `tmle` controlled direct-effect path | -0.0032 to 0.0155 | 0.9409 | 0.9797 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `rr` | marginal risk ratio, reported on the log scale | `cleverly` controlled direct-effect TMLE | -0.0025 to 0.0074 | 0.9459 | 0.9818 | pass |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `rr` | marginal risk ratio, reported on the log scale | R `tmle` controlled direct-effect path | -0.0025 to 0.0074 | 0.9459 | 0.9818 | pass |
<!-- /generated -->

## Agreement with the canonical implementation

<!-- generated: agreement -->
Comparator-backed: a paired comparison with `tmle-r-cde` on the same samples. Each row reports estimate equivalence within the declared margin, the RMSE ratio and the coverage difference, and names its comparison kind.

| law | estimand | what was compared | paired difference | share of margin used | RMSE ratio bound | coverage difference | comparison kind | calibration resolution | result |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `ate` | average treatment effect | -3.126e-10 | 3.927e-08 | 1.0000 | 0 | matching implementation | 2.202e-09 vs 0.0500 | equivalent |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `ey0` | counterfactual mean under no treatment | 3.204e-10 | 4.988e-08 | 1.0000 | 0 | matching implementation | 3.398e-09 vs 0.0500 | equivalent |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `ey1` | counterfactual mean under treatment | 7.840e-12 | 1.735e-09 | 1.0000 | 0 | matching implementation | 7.079e-11 vs 0.0500 | equivalent |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `or` | marginal odds ratio, reported on the log scale | -6.157e-10 | 3.543e-08 | 1.0000 | 0 | matching implementation | 3.092e-09 vs 0.0500 | equivalent |
| binary-outcome MAR observed law, intervention sets the intermediate to zero | `rr` | marginal risk ratio, reported on the log scale | -2.613e-10 | 2.896e-08 | 1.0000 | 0 | matching implementation | 1.672e-09 vs 0.0500 | equivalent |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `ate` | average treatment effect | 5.451e-13 | 7.861e-11 | 1.0000 | 0 | matching implementation | 5.265e-10 vs 0.0500 | equivalent |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `ey0` | counterfactual mean under no treatment | -9.426e-12 | 2.230e-09 | 1.0000 | 0 | matching implementation | 7.966e-10 vs 0.0500 | equivalent |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `ey1` | counterfactual mean under treatment | -8.881e-12 | 1.625e-09 | 1.0000 | 0 | matching implementation | 3.178e-10 vs 0.0500 | equivalent |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `or` | marginal odds ratio, reported on the log scale | 8.124e-11 | 6.819e-10 | 1.0000 | 0 | matching implementation | 6.197e-10 vs 0.0500 | equivalent |
| binary-outcome MAR observed law, intervention sets the intermediate to one | `rr` | marginal risk ratio, reported on the log scale | 6.593e-11 | 1.992e-09 | 1.0000 | 0 | matching implementation | 9.517e-10 vs 0.0500 | equivalent |
<!-- /generated -->

R `tmle` 2.1.1 constructs the observed outcome offset for its native second controlled-effect
result from `Q`, although its level-one counterfactual predictions come from `Q.Z1`. Supplying
exact, level-specific regressions therefore makes that native second result internally
inconsistent.

The registered adapter recodes each requested intermediate level to level zero,
transforms `Z` and `pZ1` together, and selects the first result. The
[`native-result2-defect.csv`](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/tmle_cde/native-result2-defect.csv)
artifact freezes the upstream failure. The standard regeneration command recreates it from the
generated sample and truth. The manifest hashes both the probe and the artifact. The comparator-backed paired table
above validates the recoded result.

## Theory properties

<!-- generated: properties -->
| property | cell | role | what was tested | what must hold | measured | result |
| --- | --- | --- | --- | --- | --- | --- |
| `cde_robustness` | `z0__all_correct` | positive | controlled direct effect at intermediate level zero: the outcome regression and all three mechanisms are correct | bias interval inside the equivalence margin, SE ratio must remain between 0.1 and 10.0 | bias -0.0073 to 0.000619, margin 0.0133, SE ratio 0.9705 | pass |
| `cde_robustness` | `z0__intermediate_wrong` | control | controlled direct effect at intermediate level zero: only the intermediate mechanism is wrong beside a wrong outcome regression | bias interval must fall entirely outside the margin, SE ratio must remain between 0.1 and 10.0 | bias 0.1628 to 0.1717, margin 0.0149, SE ratio 1.2368 | pass |
| `cde_robustness` | `z0__mechanisms_correct` | positive | controlled direct effect at intermediate level zero: all three mechanisms are correct and the outcome regression is wrong | bias interval inside the equivalence margin, SE ratio must remain between 0.1 and 10.0 | bias -0.0071 to 0.0014, margin 0.0143, SE ratio 0.9572 | pass |
| `cde_robustness` | `z0__observation_wrong` | control | controlled direct effect at intermediate level zero: only the observation mechanism is wrong beside a wrong outcome regression | bias interval must fall entirely outside the margin, SE ratio must remain between 0.1 and 10.0 | bias -0.1860 to -0.1784, margin 0.0127, SE ratio 1.3041 | pass |
| `cde_robustness` | `z0__outcome_correct` | positive | controlled direct effect at intermediate level zero: the outcome regression is correct and all three mechanisms are wrong | bias interval inside the equivalence margin, SE ratio must remain between 0.1 and 10.0 | bias -0.0038 to 0.0011, margin 0.0082, SE ratio 3.0131 | pass |
| `cde_robustness` | `z0__treatment_wrong` | control | controlled direct effect at intermediate level zero: only the treatment mechanism is wrong beside a wrong outcome regression | bias interval must fall entirely outside the margin, SE ratio must remain between 0.1 and 10.0 | bias 0.2668 to 0.2753, margin 0.0142, SE ratio 1.2345 | pass |
| `cde_robustness` | `z1__all_correct` | positive | controlled direct effect at intermediate level one: the outcome regression and all three mechanisms are correct | bias interval inside the equivalence margin, SE ratio must remain between 0.1 and 10.0 | bias -0.0031 to 0.0039, margin 0.0117, SE ratio 0.9643 | pass |
| `cde_robustness` | `z1__intermediate_wrong` | control | controlled direct effect at intermediate level one: only the intermediate mechanism is wrong beside a wrong outcome regression | bias interval must fall entirely outside the margin, SE ratio must remain between 0.1 and 10.0 | bias -0.1665 to -0.1581, margin 0.0140, SE ratio 0.8776 | pass |
| `cde_robustness` | `z1__mechanisms_correct` | positive | controlled direct effect at intermediate level one: all three mechanisms are correct and the outcome regression is wrong | bias interval inside the equivalence margin, SE ratio must remain between 0.1 and 10.0 | bias 0.000193 to 0.0097, margin 0.0159, SE ratio 0.9940 | pass |
| `cde_robustness` | `z1__observation_wrong` | control | controlled direct effect at intermediate level one: only the observation mechanism is wrong beside a wrong outcome regression | bias interval must fall entirely outside the margin, SE ratio must remain between 0.1 and 10.0 | bias -0.1797 to -0.1727, margin 0.0118, SE ratio 1.5008 | pass |
| `cde_robustness` | `z1__outcome_correct` | positive | controlled direct effect at intermediate level one: the outcome regression is correct and all three mechanisms are wrong | bias interval inside the equivalence margin, SE ratio must remain between 0.1 and 10.0 | bias -0.0025 to 0.0037, margin 0.0105, SE ratio 1.1461 | pass |
| `cde_robustness` | `z1__treatment_wrong` | control | controlled direct effect at intermediate level one: only the treatment mechanism is wrong beside a wrong outcome regression | bias interval must fall entirely outside the margin, SE ratio must remain between 0.1 and 10.0 | bias 0.2137 to 0.2195, margin 0.0099, SE ratio 2.3230 | pass |
| `interval_calibration` | `z0__correctly_specified` | positive | controlled direct effect at intermediate level zero: all four required nuisance functions 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 0.9363 to 0.9474, SE ratio 0.9726 to 1.0056, empirical efficiency ratio 0.9841 to 1.0167, reported efficiency ratio 0.9873 to 0.9910 | pass |
| `interval_calibration` | `z0__noise_control` | control | controlled direct effect at intermediate level zero: one efficiency-bound unit of independent noise is added to each estimate | the empirical efficiency ratio must rise above the band | coverage 0.8249 to 0.8425, SE ratio 0.6937 to 0.7174, empirical efficiency ratio 1.3788 to 1.4259, reported efficiency ratio 0.9873 to 0.9911 | pass |
| `interval_calibration` | `z0__shrunken_se_control` | control | controlled direct effect at intermediate level zero: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8099 to 0.8281, SE ratio 0.6810 to 0.7039, empirical efficiency ratio 0.9839 to 1.0167, reported efficiency ratio 0.6911 to 0.6937 | pass |
| `interval_calibration` | `z1__correctly_specified` | positive | controlled direct effect at intermediate level one: all four required nuisance functions 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 0.9352 to 0.9463, SE ratio 0.9789 to 1.0133, empirical efficiency ratio 0.9767 to 1.0102, reported efficiency ratio 0.9876 to 0.9910 | pass |
| `interval_calibration` | `z1__noise_control` | control | controlled direct effect at intermediate level one: one efficiency-bound unit of independent noise is added to each estimate | the empirical efficiency ratio must rise above the band | coverage 0.8212 to 0.8389, SE ratio 0.6913 to 0.7147, empirical efficiency ratio 1.3845 to 1.4311, reported efficiency ratio 0.9875 to 0.9910 | pass |
| `interval_calibration` | `z1__shrunken_se_control` | control | controlled direct effect at intermediate level one: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8174 to 0.8353, SE ratio 0.6856 to 0.7098, empirical efficiency ratio 0.9759 to 1.0099, reported efficiency ratio 0.6913 to 0.6937 | pass |
| `power` | `z0__alternative` | positive | controlled direct effect at intermediate level zero: the same test applied to a law with a real effect | rejection lower bound clears the minimum power | rejection 0.9988, 0.9907 to 1.0000 | pass |
| `power` | `z1__alternative` | positive | controlled direct effect at intermediate level one: the same test applied to a law with a real effect | rejection lower bound clears the minimum power | rejection 1, 0.9934 to 1 | pass |
| `root_n_and_efficiency` | `z0__n_2000` | positive | controlled direct effect at intermediate level zero: bias, coverage and SE calibration at n = 2,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000936, coverage 0.9160 to 0.9431, SE ratio 0.9664 | pass |
| `root_n_and_efficiency` | `z0__n_500` | control | controlled direct effect at intermediate level zero: bias, coverage and SE calibration at n = 500 | coverage interval lies below nominal or clears the declared floor | bias 0.0034, coverage 0.8921 to 0.9229, SE ratio 0.9441 | pass |
| `root_n_and_efficiency` | `z0__n_8000` | positive | controlled direct effect at intermediate level zero: bias, coverage and SE calibration at n = 8,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000563, coverage 0.9402 to 0.9630, SE ratio 1.0157 | pass |
| `root_n_and_efficiency` | `z1__n_2000` | positive | controlled direct effect at intermediate level one: bias, coverage and SE calibration at n = 2,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias 0.000763, coverage 0.9196 to 0.9462, SE ratio 0.9613 | pass |
| `root_n_and_efficiency` | `z1__n_500` | control | controlled direct effect at intermediate level one: bias, coverage and SE calibration at n = 500 | coverage interval lies below nominal or clears the declared floor | bias 0.0027, coverage 0.8868 to 0.9183, SE ratio 0.9120 | pass |
| `root_n_and_efficiency` | `z1__n_8000` | positive | controlled direct effect at intermediate level one: bias, coverage and SE calibration at n = 8,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000502, coverage 0.9462 to 0.9678, SE ratio 1.0324 | pass |
| `root_n_rate` | `z0__empirical_sd` | positive | controlled direct effect at intermediate level zero: 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 -0.5302 to -0.4933 | pass |
| `root_n_rate` | `z0__reported_se` | positive | controlled direct effect at intermediate level zero: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.4881 to -0.4817 | pass |
| `root_n_rate` | `z1__empirical_sd` | positive | controlled direct effect at intermediate level one: 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 -0.5476 to -0.5104 | pass |
| `root_n_rate` | `z1__reported_se` | positive | controlled direct effect at intermediate level one: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.4875 to -0.4815 | pass |
| `targeting_necessity` | `z0__targeted` | positive | controlled direct effect at intermediate level zero: the estimator fluctuates a misspecified outcome model, so targeting does all the adjusting | bias interval inside the equivalence margin | bias -0.0051 to 0.0030, margin 0.0137 | pass |
| `targeting_necessity` | `z0__untargeted` | control | controlled direct effect at intermediate level zero: the identical fit with every fluctuation step removed | bias interval must fall entirely outside the margin | bias -0.0828 to -0.0819, margin 0.0016 | pass |
| `targeting_necessity` | `z1__targeted` | positive | controlled direct effect at intermediate level one: the estimator fluctuates a misspecified outcome model, so targeting does all the adjusting | bias interval inside the equivalence margin | bias 0.000291 to 0.0097, margin 0.0158 | pass |
| `targeting_necessity` | `z1__untargeted` | control | controlled direct effect at intermediate level one: the identical fit with every fluctuation step removed | bias interval must fall entirely outside the margin | bias -0.0530 to -0.0518, margin 0.0020 | pass |
| `type_i_error` | `z0__sharp_null` | positive | controlled direct effect at intermediate level zero: a confounded law whose true contrast is exactly zero | one-sided rejection bound stays under the declared type-I ceiling | rejection 0.0537, 0.0353 to 0.0777 | pass |
| `type_i_error` | `z1__sharp_null` | positive | controlled direct effect at intermediate level one: a confounded law whose true contrast is exactly zero | one-sided rejection bound stays under the declared type-I ceiling | rejection 0.0550, 0.0363 to 0.0792 | pass |
<!-- /generated -->

The robustness grid checks the actual four-nuisance contract at both intermediate levels. A
correct outcome regression must rescue wrong treatment, intermediate, and observation mechanisms;
with a wrong outcome regression, all three mechanisms must be correct. Three separate controls
make exactly one mechanism wrong. Further cells test root-n contraction, exact-law efficiency,
interval calibration and its two controls, type-I error and power, and whether targeting materially
changes the plug-in.

The level-one mechanisms-correct cell has a resolved finite-sample bias at `n = 2,000`. Its 99%
bias interval is 0.000193 to 0.0097, which remains inside the declared 0.0159 margin.

## Measured values and declared margins

| quantity | value | source |
| --- | --- | --- |
| `replicates` | 3200 | paired replications |
| `n` | 2000 | observations per primary replication |
| `independent_tests_passed` | 20 | truth tests passing |
| `independent_tests_total` | 20 | truth tests reported |
| `paired_tests_passed` | 10 | paired comparisons passing |
| `paired_tests_total` | 10 | paired comparisons reported |
| `property_cells_passed` | 36 | property cells passing |
| `property_cells_total` | 36 | property cells reported |
| `max_standardized_bias` | 0.0685 | largest primary standardized bias |
| `min_coverage` | 0.9216 | lowest primary coverage |
| `max_margin_utilization` | 4.988e-08 | largest paired similarity-margin share |
| `margin:confidence_level` | 0.9900 | Monte Carlo confidence level |
| `margin:alpha` | 0.0500 | nominal 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:union_model_se_lower` | 0.1000 | union-model SE-ratio screen, lower limit |
| `margin:union_model_se_upper` | 10 | union-model SE-ratio screen, upper limit |
| `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 |
| `margin:rmse_noninferiority` | 1.1000 | RMSE-ratio noninferiority bound |
| `margin:coverage_noninferiority` | -0.0250 | coverage-difference noninferiority bound |
| `margin:calibration_noninferiority` | 0.0500 | calibration-excess noninferiority bound |
| `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:efficiency_ratio_lower` | 0.9000 | efficiency-ratio lower bound |
| `margin:efficiency_ratio_upper` | 1.1000 | efficiency-ratio upper bound |
| `margin:shrunken_se_factor` | 0.7000 | negative-control SE multiplier |
| `margin:targeting_displacement` | 0.2500 | minimum targeting displacement |
| `bound:z0_standard_error` | 0.0524 | exact level-zero ATE efficiency bound at n = 2,000 |
| `bound:z1_standard_error` | 0.0457 | exact level-one ATE efficiency bound at n = 2,000 |

## Limits

- The study covers binary treatment, binary intermediate and outcome, one three-level baseline
  covariate, and an observational MAR response mechanism with no post-treatment confounder between
  treatment and the intermediate.
- Exact finite-support nuisances isolate targeting and inference. The study does not validate
  flexible learner wrappers or cross-fitting.
- The level-zero untreated mean has 0.9216 primary coverage at `n = 2,000`. This matches R
  and is about six Monte Carlo standard errors below 0.95. The observed
  `(A=0, Z=0, W=0, Delta=1)` stratum has expected count 31.25 and clever-covariate weight 32.
  The shared 0.90 coverage floor treats this finite-sample undercoverage as acceptable.
- The comparator requires level recoding because of the frozen native second-result defect in R
  `tmle` 2.1.1. The registered probe recreates the defect during standard regeneration. The study
  does not claim that the native result is valid with exact `Q.Z1` inputs.
- Inference is pointwise. The study does not cover simultaneous bands, active probability bounds,
  weights, clusters, multi-arm treatment, continuous intermediates, or MNAR outcomes. The [default-band study](default-simultaneous-bands.md) measures the default band of this study's subject fit at each intermediate level. The cell at Z = 0 is red.
- `ATT` and `ATC` retain exact-law Gateaux and remainder evidence but are absent here because R
  `tmle` does not report them on its controlled direct-effect path.
- This is not evidence for natural direct or indirect effects, nor for a general longitudinal
  intervention with treatment-induced intermediate confounding.

## Reproduction

The [fixture README](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/tmle_cde/README.md),
[manifest](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/tmle_cde/manifest.json),
[native-result probe](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/tmle_cde/probe_native_result2.R),
[native-result artifact](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/tmle_cde/native-result2-defect.csv),
[replications](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/tmle_cde/replicates.csv.gz),
[paired decisions](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/tmle_cde/equivalence.csv),
and [property results](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/tmle_cde/properties.csv)
carry the protocol, provenance, and every published row.