Scoped negative result: same-slot helper470 retirement raises the complete bit bill

[1337isnot1337]

Status: scoped negative result and exact interval replay. No new κ or supplier adoption.

Mathematical correction

Commit 93db17f corrects the integral identity and the following positivity bound by restoring the missing factor (1-a): if S_r denotes the displayed sum of integrals, the identity is Q_r = (1-a) S_r, not Q_r = S_r. Since 1-a > 0 on the stated domain, the corrected lower bound remains positive. All 57 exact-rational checks pass with this correction.

This adds a complete same-slot price audit for PR #1256's finite helper470 exception. Shrinking its existing width-eight slot to width seven and returning the freed rank to that slot's idle remainder changes the paid histogram by e1 + e5 - e7 + e_(r+1) - e_r (with the zero-remainder case handled separately). For the frozen width-64 interface, the raw moment strictly increases for every feasible old remainder r=0..56; the inherited per-call surcharge also rises.

At the pinned selected exponent, the registered exact-rational replay checks all 57 remainders and rebuilds the complete selected profile for actual old classes 2, 4 and 6. The full bill increases in all three cases. Omitting the returned rank gives a false favorable control. PR #1256's distinct two-slot relaxation remains favorable at all three actual classes, so this result does not subsume or refute that mechanism.

Exact base: bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Four live source inputs are SHA256 and Git-blob pinned in research/bit-inplace-retirement-seed11/SOURCES.json; the selected review used to scope predecessor claims is pinned there as provenance.

Reproduce from the repository root with Python 3.12:

python3.12 scripts/research_package.py --package research/bit-inplace-retirement-seed11

Expected: PASS_REGISTERED_RESEARCH_PACKAGE research/bit-inplace-retirement-seed11 outcome=negative-result.

The conclusion applies only to this profile change and the frozen inherited moment formula. It does not claim supplier admission, a new bit endpoint, a new κ, or an asymptotic theorem. Physical owner/window admission, H4 cleanup, native recursive replay, precision/tape and outer assembly remain open.

Credit: Ali Romman's PR #1043 for the earlier source-boundary deletion and hosted invoice; PR #1048 for the research direction, with its general fixed-exponent root-ordering claim rejected by the pinned selected review; PR #1256 for the finite restoration exception and two-slot relaxation; PR #1302 for native replay and full-frame closure; and PR #555 plus its cited lineage for the tuned bit word. Prepared by Cinna Davis (@1337isnot1337) with substantial OpenAI Codex assistance in review, derivation, exact interval implementation and writing. New work is Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at c4f3e9ae15bfc9c358af79bf023ae046961be499.

This remains open after scoped triage. Next review step: The all-exponent proof omits the factor (1-a): Q_r=(1-a) times the displayed sum of integrals, not that sum itself. Correct the equality and following lower bound; positivity survives because 1-a>0. Exact selected-moment checks pass, but the published inequality as written is false.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.

[1337isnot1337]

@Mister-Meeseeks Thanks for identifying the missing factor. Commit 93db17f corrects the identity to Q_r = (1-a) times the displayed sum of integrals and carries that same factor into the following lower bound. Because 1-a > 0 on the stated domain, the corrected bound is still positive. The exact-rational verification covers all 57 cases and passes. I have updated the PR description to state the correction and scope.