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Exclude Type A rank-137 productive root splits (0% κ change) - #7316

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ToikY:codex/p104-rank137-productive-root-bound
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ToikY wants to merge 3 commits into
CrocSwap:mainfrom
ToikY:codex/p104-rank137-productive-root-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%. Under the exact #7113 caller and complete #7277 invoice, both Type A rank-137 roots fail to admit a positive two-factor split at any literal cut. The coordinate screen checks 9,568 root-boundary cases at both body-one phase signs. All 241 provisional interior cases fail the exact signed Laurent gate. The full original 72-field endpoint is verified.

Allowing an invertible q-even ordinary basis within a port requires a squarefree body mask and common central parity across all nonzero terms in the full root column. Independent forward and reverse replays match all 9,568 cases. There are 8,383 mixed body masks, 913 mixed phase parities and 272 zero-rank sides. Zero cases survive or remain unresolved.

The directed price retains all paid jobs and includes all 17 native copies. The optimistic compatible-stock upper across both roots is about 65.2479130965 raw units before added costs. The necessary support gate leaves zero compatible saving. The fixed #7277 comparison is κ = 0.003645669928698.

Task and overlap

Rounds 54–55 of Discussion #7111, checkpoint. Canonical base e545235, comparator #7277 at ed090b5 and caller #7113 at 07a76c5. #7314 at 9d0119e changes helper 863’s funded return and the paid route of role 1355. Here all paid caller operations stay fixed. #7243 examines older native chart cuts, #7313 charged native rank-six helpers, and #7315 Type B paid-idle grouping. The branch retains both published #7257 hosted-replay prerequisites with original authorship.

Validation

From a clean checkout with CPython 3.12 and assertions enabled:

python3.12 -B scripts/research_package.py --package research/p104-rank137-productive-root-bound
python3.12 -B scripts/check_research_commit.py --package research/p104-rank137-productive-root-bound --check-modes --check-source-history

Registered replay, source/byte/mode authentication, Git-free export replay and six navigation tests passed locally. The standalone replay regenerated all nine receipt hashes and rejected altered caller and body-one inputs. Hosted historical replay is pending at submission.

Credit

#7113 supplies the exact signed caller, #7277 the complete invoice, #7298 the pricing and profile reconstruction, and #7315 the related projector lineage. Discussion #7111 records earlier caller layout work with changed paid supports. OpenAI Codex and subagents materially assisted.

Open next questions

Changes to paid chronology and alternative signed child interfaces are outside the tested scope. The package records the necessary column condition and the exact checks needed to turn a later surviving price into a complete caller candidate.

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