iter 11 — the contested item resolves GROUNDED

Attack item R-5 · 2026-07-30 · harness harness/subslice_null_pivotality.py

The one contested item in the campaign, and why it was stuck

KB.md carries exactly one CONTESTED entry: one research section says standardise each sub-slice reading by its own length (free, zero parameters); another says fixed-b asymptotics make the sub-slice p-value non-pivotal, so no standardisation recovers a calibrated comparison. Resolving it was blocked by a MUST-NOT-ASSUME:

"The fixed-b refutation is second-hand and about the sample mean. It rests on one sentence in Shao & Politis citing Lahiri (2001), which was not retrieved. ξ is not a sample mean." — research gap #962

That paper is unavailable. But the question it was being used to answer — does a closed-form standardisation recover comparability between sub-slice lengths for ξ — is directly measurable. Measuring it does not require the citation.

Result — 2,000 replications per arm, n=3,990, under independence

The resolution, and it is better than either side

√k scaling holds in all four arms, and shape is preserved in all four. The only thing that changes with sub-slice length is the √k factor. So:

A standardisation DOES recover comparability between sub-slice lengths for ξ. The sub-slice rule is repairable, not necessarily deletable — established empirically, for ξ, without the Lahiri citation.

That supports the c.6 position. But §(b)'s suspicion was not baseless — it was right for a different reason than it gave:

The standardising constant is not universal. τ² depends on the law of Y exactly as Chatterjee Thm 2.2 warns: 2/5 continuous → ≈0.476 at 5 levels → 1.0 for Bernoulli(½). Hard-coding 2/5 would understate the sd by 58% on a binary-valued kernel.

The measured z_sd of 1.580 for Bernoulli(½) matches Thm 2.2's predicted √(1/0.4) = 1.581 to three decimals — the theorem reproduced, not merely cited.

My prediction was wrong, and the way it was wrong is the finding

I predicted 30.9% ties would break the 2/5 constant. It did not break — z_sd stayed 0.991–1.009. My offered explanation was that 30.9% ties still leaves ~2,760 distinct Y values out of 3,990, so Y is "nearly continuous". Asserting that explanation without testing it would have been exactly the move this loop exists to prevent, so the 5-level and binary arms were added. They confirm it: the break needs severe discreteness, not a high tie fraction.

The concrete consequence for this cascade

• LINKUSDT@100 is in the safe zone. The tie-heaviest real cell measured (30.9%) sits where 2/5 holds to within 1%. The campaign's worry about that cell does not extend to this constant.
• Sign-valued kernels are exactly where a hard-coded 2/5 would be badly wrong. bar_sign_markov_flux is a shipped column built on signs — a 2-level substrate, where the correct constant is 2.5× larger. Any repair that assumes 2/5 would be most wrong precisely on the kernels the campaign is screening.
• The fix already exists in the theory. Chatterjee Thm 2.3 gives a consistent O(n log n) plug-in τ̂²ₙ. The research confirmed it exists; this measurement shows it is necessary, not optional.

What changed

Nothing in the instrument. This resolves a contested reading and identifies which repair is sound — standardise per length, but estimate τ² rather than assume it. Applying that repair is parameter-bearing in practice (it changes every sub-slice comparison) and remains the operator's call. The KB entry can move from CONTESTED to resolved-with-a-caveat.

Limits

• Independence only. All four arms are null-case; whether the √k scaling survives under strong dependence was not tested, and the guard compares readings from cells that are not at the null.
• Ties in Y only. X-ties introduce the estimator randomisation studied in iters 2–3, which is a separate mechanism and is excluded here by construction.
• Contiguous splits of i.i.d. data. Real sub-slices are contiguous blocks of an autocorrelated series, which is the exact condition the fixed-b argument was about. This shows the length effect is a clean √k; it does not settle whether serial dependence adds a further distortion. That part of §(b) stands unresolved.

Evidence: harness/subslice_null_pivotality_evidence.json. Reproduce: VIRTUAL_ENV="" uv run --python 3.13 --no-project --with numpy --with pandas python3 harness/subslice_null_pivotality.py