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Exclude fixed-word singleton P104 helper splits (0% κ change) - #7303

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ToikY:codex/p104-singleton-helper-split-bound
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ToikY wants to merge 3 commits into
CrocSwap:mainfrom
ToikY:codex/p104-singleton-helper-split-bound

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@ToikY

@ToikY ToikY commented Nov 11, 2026

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Change and mathematical scope

NO VERIFIED GAIN. Exact conditional κ change 0%. The exact #7277 word has no singleton productive helper split at an existing strict intermediate chart with fixed chronology and endpoint rescalings alone. The census covers 1,101 helpers, 1,396 chart triples and 11,489 representative cuts. An independent replay uses a different prime and checks all 74 prefix matches over the rationals. Every corresponding suffix fails.

For one fixed-mass two-way split of rank at most nine, the gross moment gain across all 17 copies is at most 153/199 for 0 ≤ κ ≤ 1/200. A new positive-rank paid child costs at least one. This bound grants added ordinary work free and assumes no paid removals. Multiple splits and changes in rank mass are outside its scope.

Task and overlap

Changed productive inventory scope on canonical e545235. The strongest independently reproduced comparable κ remains 0.003645669928698 on #7277 at ed090b5. #5599 and #7110/#7112 supply cocharted constructions, #5718 permits distinct boundary corrections, #7121/#7130 supply exact successor constructors, #5702/#7175 price older fixed-mass refinements, and #7299 prices general rank-dependent fees. #7142 changes target rank mass through a charged extension.

Validation

From a clean checkout using CPython 3.12 and assertions enabled:

python3.12 -B scripts/research_package.py --package research/p104-singleton-helper-split-bound
python3.12 -B scripts/check_research_commit.py --package research/p104-singleton-helper-split-bound --check-modes --check-source-history

Registered replay, committed bytes/modes/source history, navigation, official export and empty-PATH Git-free replay passed. Controls cover a reciprocal-rescaling positive case, prefix and suffix contamination, duplicate manifest keys and an altered source word. The branch inherits the two exact #7257 replay prerequisites. No physical candidate was built.

Credit and open next questions

#7277 supplies the exact native word and #7113 the complete signed caller. The README preserves the predecessor scope and credit. OpenAI Codex and subagents materially assisted.

Mixed cocharted bases and changed boundary contracts remain open. The charged endpoint route can be tested first by repricing a single new rank-one payment and its exact target debits and credits, then applying the joint prefix and suffix support gate.

Clear1nsight and others added 3 commits November 11, 2026 15:39
This is the exact documentation prerequisite retained by CrocSwap#7156. It points the onboarding check to the selected CrocSwap#7000/CrocSwap#7001 review. Credit to Rohan Arun and the source authors.
The PR CrocSwap#6292 rejection census and package plan are statements about 2485805. Load its exact sources and planner in a private sparse checkout, keeping all source hashes, 19 expected rejections, nine package selections and the empty-plan control. Subsequent edits to the live Makefile and CI guide no longer invalidate this historical check.

The original audit is by unpaidmoon, building on Dennis’s historical replay gate. The pinned repository view follows the precedent of Matarener’s PR CrocSwap#5434. Repair prepared with substantial OpenAI Codex assistance.
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2 participants