[commdata2338]

Change and mathematical scope

Independently certify the fixed PR2575 owner evacuation against PR2530, and prove the exact range where it lowers the recursive rank bill. Both 281,052-role allocations pass the literal window, width, family and slice constraints. The evacuation moves 547 whole-helper occurrences between bins, changes 694 role descriptors and 462 residual ranks, preserves rank mass, and adds 56 positive-rank children.

For F(p) = sum_r (H2575[r]-H2530[r])*r^p, there is exactly one zero in 0<p<1, with 0.289994 < p_* < 0.289995. The new rank bill is strictly lower for p_*<p<1, and strictly higher below p_*. The initial all-exponent-dominance question is therefore answered negatively; the useful completed result is the exact crossover classification. This does not identify an error in PR2575's stated endpoint.

The proof uses the signed hinge function sum d_r min(r,t), its single sign change at 57/29, and a strictly decreasing normalized integral. Rational logarithm/Taylor enclosures certify the bracket signs. No floating-point sign decision or approximate root is an acceptance condition.

Only research/t74-evacuation-power-audit/ is added. This is a finite allocation certificate and scoped analytic proof. No new supplier, endpoint, κ, optimizer minimum, selected-frontier change or full multiplication theorem is claimed. Native dirty-state/phase replay, physical chart realization, complete movement/precision charges and outer admission remain inherited and unchecked here.

Task and overlap

The claim is in discussion #2616. Main was fetched at entry and again at 2026-10-15 16:29:41 UTC, and remained 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. The two dependency heads also remained unchanged:

• PR2530, @zxv: b4012098048e12500b2d33d2e84be281915a27ac.
• PR2575, @jeremykothe2: 921c229b4f030121a1d305de6259e174cd391955.

Priority revision 5 (main b4560d9e7216f72b73c5aa940ac099c05e33ccf9, 2026-10-15 16:31:36 UTC) landed after that check. It changes guidance documents only and leaves the independent-moment card, both heads above and this package's base-commit pins unchanged.

The source index pins all 19 retained files by exact upstream path, commit, Git blob and SHA256. Both complete BORROW-WORD JSON objects agree between the sources, as do order and dispatch. Helper endpoint dimensions are independently derived from complete GF(2)^9 vector sets. Local paid profiles are source-reported common quantities; their internal frame invoice is not independently rederived here and cancels in the comparison.

Task card:

• Task ID / scope key: independent-moment; PR2575-vs-PR2530/actual-owner-evacuation/single-power-crossover/complete-map-legality. Recorded card retrieval nonce 59eb0b25697209d2f3021d0193fc238a, catalogue key c6f2494b197df3bc3591.
• Base and exact predecessors: the main and two heads above; PR2559 is the credited evacuation-method predecessor, not an executed dependency.
• Concrete object and question: the two fixed whole-helper maps, their actual chronological legality and their rank power-sum difference for all real 0<p<1.
• Scope status: refined. A live central dirty-borrowing record supplies a specific independent-audit target. The initial uniform-dominance hypothesis fails; the same-object crossover classification completes the audit.
• Exact claim audited: PR2575's allocation and claimed rank-cost improvement; the added all-exponent question is ours, not a claim attributed to PR2575.
• Method and bounded domain: all 666 calls, all 281,052 roles per map, all 149,184 bins per map; integer event positions/occupancy, exact endpoint subspaces, rational enclosures and an analytic integral argument. No alternative-fill search.
• Nearest overlap: PR2530 constructs the words/fill; PR2575 constructs and already checks the evacuation; PR2559 supplies the method. Discussion CLAIM: PR2530 source-partner handoff cuts, independent dirty-lender audit #2606 audits lender values; Discussion CLAIM: PR2588 swapped aliases, independent chronological frame and local-moment audit #2605/PR2588 audits changed local labels; Discussion CLAIM: T74 diagonal order, chronological whole-helper packing bounds (PR2571 residual) #2608/PR2571 seeks a chronology lower bound. Discussion Cost-aware source-partner helper assignments above PR2588 #2612 searches new assignments. None is this fixed-map crossover comparison. Existing allocation checks are explicitly corroboration.
• Cost budget / observable result: include every changed idle residual, bind common words and dispatch, and identify the sign of the complete recursive rank-cost delta. Unexamined movement/precision/outer charges are not assumed equal.
• Evidence / stop test / cap: finite receipt, full proof, nine semantic controls, four integrity controls; bounded 60-minute session, no full supplier or new-record construction.
• Credit / artifact / reproduction: credited below; package README, RESULT and source index; python3 -I -B scripts/research_package.py --package research/t74-evacuation-power-audit.

Final cached overlap covered 812 open PRs (2026-10-15 16:22:35 UTC), 1,276 Discussion records (16:27:10 UTC), and the older 799-PR changed-path index (15:59:04 UTC), with complete reported pagination. Offline freshness warnings and truncated PR file lists remain explicit in OVERLAP.json; these checks are not a novelty certificate. Exact relevant heads were fetched separately.

Validation

Passed on CPython 3.12.3 / Linux x86_64, standard library only:

python3 -I -B scripts/research_package.py --package research/t74-evacuation-power-audit
python3 -I -O -B research/t74-evacuation-power-audit/verify.py
python3 -I -B scripts/research_package.py --package research/t74-evacuation-power-audit --check-only

Expected primary output:

PASS_T74_EVACUATION_POWER_AUDIT roles_per_map=281052 changed_bins=462 crossover=(0.289994,0.289995) controls=9

The primary replay reconstructs all 1,332 physical windows from 2,220 per-replica events, including 666 bridges, and checks all eleven emitted owner fields. Nine controls reject missing/ill-typed roles, invalid offsets/windows, family aliasing, overlapping slices, prefix holes, reversed cost direction and lost rank mass. Reversed row order preserves the result; independent integer square roots corroborate the interval evaluator.

The registered integrity check passes source-byte mutation, JSON value-type mutation, exclusive-output refusal and a Git-free read-only export, with all exported bytes unchanged. All 19 vendored files were also compared directly with their exact upstream Git objects. Metadata/source pins and staged whitespace checks pass. Ordinary replay writes no tracked files; receipt regeneration refuses existing outputs.

Not run: the predecessor's full native/supplier/outer cold replay, physical Clifford/projector checks, full precision/stock/bit-side admission, Lean, hosted CI or independent human review. The proof is a written analytic argument with exact finite hypotheses, not a proof-assistant theorem.

Credit

Jeremy Kothe (@jeremykothe2), PR2575, produced the evacuated fill. Philippe Van Velzen (@philippeVV), PR2559, introduced evacuation. @zxv, PR2530, supplied the eight source-partner aliases, both words, the diagonal order and starting allocation. Cinna Davis (@1337isnot1337), PR2226, introduced anticipatory dirty borrowing; Tekalign (@tekuuu), PR2436, Vlado Vojdanovski, PR2322, and the retained T74/native/controller lineage remain credited. Existing allocation checks and the elementary integral/sign-change method are not claimed as new inventions. Source notices and Apache-2.0 licensing are retained.

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

The README and TASK.json identify two bounded follow-ups: test one legal same-word evacuation whose signed hinge function is nonpositive at every knot, or compare an existing alternative spectrum while keeping words and order exactly fixed. These would distinguish uniform concave-cost dominance from optimization at one exponent. Both need an actual legal replacement and source-bound allocation checks before any full supplier or κ claim.

Workflow feedback (optional)

The overlap helper, exclusive handoff reservation and source-word equality checks made a distinct central audit feasible. A short machine-readable list of changed owner bins and explicitly intended exponent range would make evacuation submissions easier to compare. This is optional supporting evidence, not a proposed new admission requirement.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG