# What the validation programme established

The active registered [canonical DR-TMLE study](../method-evidence/canonical-dr-tmle.md)
now adds a theory-first comparison with pinned R `drtmle` on the paper's binary complete-data law.
Most paired cells establish bounded equivalence, but none establishes the prespecified
coverage-superiority route; one paired cell is inconclusive. The both-correct calibration and
root-n cells pass, while both one-correct robustness cells fail their finite-sample bias rule.
Those red results are committed evidence, not exceptions to the theorem: the theorem remains
conditional on rate and remainder premises that a fitted dataset cannot certify.

The older drift-law programme below asks a different, harder question. It is retained as
historical evidence rather than silently generalized to the registered paper law.

This page's claims rest on a closed programme of six pieces: a theoretical audit against the
sources, a targeting-and-exit study, a controlled coverage demonstration, a reference study for
the reduced regressions, a construction ablation, and a terminal experiment. The
[evidence index](../evidence.md) records the acceptance instruments. The
programme itself, including its study harnesses, replicate records, differential diagnostics,
dispatch workflows, and working notes, is archived at the `drtmle-validation-archive-2026-08` tag
rather than on `main`. In summary:

**Established.** The implementation is faithful to Theorem 1 in five respects.

- The corrected curve is the Gateaux derivative of the parameter.
- The sign of the mechanism correction is the appendices' orientation.
- The reported variance is Theorem 1's.
- The three score equations are solved at the state returned.
- The interval beats a plain TMLE's by a material margin in the drift cells,
  on that design. It does not show validity.

**Not established in that archived drift-law programme, and recorded as such.** Three things.
Nominal coverage anywhere in that study,
the best reading being `0.880`. A localized cause for that shortfall: a six-contrast construction
ablation over 2,496 fits returned a **null** on its primary column, and a terminal experiment over
both a selection and an independent audit cohort nominated **nothing**. And any `src/` change
justified against the theorem.

The reported `se` runs about 10% short of the spread it covers in one drift cell, and about 16%
*long* in the other. The programme attributed the shortfall to a second-order remainder that does
not vanish at these sizes. A committed probe, `reviews/rm40/drift_attribution.py`, tested that
reading under a rule fixed before it ran. The shortfall is not attributed. The conditioning term of the
inconsistent nuisance, evaluated at the mean fit, does not account for it.

| cell | predicted root-n bias | archived root-n bias | probe outcome |
| --- | --- | --- | --- |
| `g-drift` | -0.067 | +3.33 | refuted |
| `q-drift` | +0.021 | +1.44 | refuted |

The `g-drift` mechanism learner converges to an additive approximation of `g_0`, so that cell is
not inside Theorem 1's union condition. The probe measures that error as 0.002 in the L2 norm.
The probe log also reports a sensitivity row that the rule does not score. It averages the term
over the fits, so it includes the random part of the mechanism fit. It predicts +1.70 for
`g-drift`, about half of the archived +3.33. The rule would read that row as inconclusive.

That is why the release claim is conditional validity, and why the conditions are stated on this
page rather than assumed away.