Audit P104 helper histories with endpoint span constraints

[kumagi]

Change and mathematical scope

A P104 history profile can pass the current crossing, endpoint-count and cost relaxations without enough endpoint geometry. This package proves two necessary histogram rows—total arrival dimension and departure codimension are each at least 832—under the frozen X-only, monotone ZERO-to-FULL relay contract. A concrete 400-lifetime profile 329*(1,7,1) + 71*(1,1,1,1,1,1,1,1,1) passes the earlier cut bounds (4873 each), reported lifetime-count floors and certified favorable cost bound (upper 0.999470826199440), but scores only 826 in both new rows.

A 406-lifetime control passes the new rows, so this is one profile exclusion and a reusable necessary screen, not a new universal lifetime floor or P104-route rejection. No construction, complete supplier invoice, frontier change or new exponent is claimed. Compatible frames, chronology, coefficients, physical owners, precision and the complete consumer remain open.

Task and overlap

Task supplier-boundary-audit, scope key dcdb0fa8e49b08a958d0, priority revision 5. Scope is changed from the card's selected-supplier wording to the pending P104 supplier's explicitly prioritized endpoint/routing obligation. The selected binding baseline and card's historical owner-audit example passed as orientation controls.

Started from canonical main ffbd90dd90dbe0055464f3a1411b25a3a4fdc6b8; publication rebased onto refreshed main 38746ad3f6ffebcc0275e286b1dbb733d7c696dd. Guidance, priority revision, selected record and all declared inputs were unchanged. Scientific pins remain at the starting main.

Nearest work: #2353 (rank-eight target support), #2614 (later-source reads), #2640 (seven crossing constraints), #2675 (coupled cost relaxation), #2682 (proper endpoint arrivals). Exact heads and authors are in TASK.json/PROOF.md. This supplies one geometry coupling requested by #2682, not a bug report against its correctly scoped relaxation.

The newer Sagar Thakrar mixer handoff, fork commit 743640530229e1821ae11dc104798871272d6f00, already excludes the historical 208-lifetime example. This package credits that overlap and leads with the 400-lifetime profile, which passes its reported count floors. No independence from all structural facts in that handoff is asserted.

Final overlap covered all 486 open PRs, 2,097 closed/merged PRs and 1,543 Discussion records, refreshed 2026-10-16 07:36–07:37 UTC. Focused follow-up found own claim/package plus an unrelated endpoint-span note. Search omits code diffs/arbitrary nested files and is not proof of novelty. Canonical claim.

Validation

• CPython 3.12.13 registered replay: python3.12 -B scripts/research_package.py --package research/p104-endpoint-span-audit — PASS. Both commands use -I -O -B and explicit exceptions.
• CPython 3.14.4 direct optimized runs of both scripts — PASS.
• Independent binary-elimination checker reconstructs 104 rank-eight arrival spans and 104 rank-eight departure spans, 4,992 demands, 336 later-readable pairs, no direct bypass and all 256 positive-composition histories. It imports no primary/predecessor checker.
• Primary checker reuses authenticated PR2675 geometry and Douglas Colkitt's exact rational cost engine, executing their source bytes directly. Controls distinguish zero-weight visits, asymmetric endpoint rows, the rejected 400 profile and surviving 406 control.
• Metadata/source pins, exact committed bytes (17 files) and whitespace checks — PASS. Registered replay rerun after rebase.

The universal implication is in PROOF.md; finite checks do not prove all possible relay programs by enumeration. No selected cold replay, full native supplier replay, mixer-fork replay, new LP optimization, proof assistant or independent human review is claimed.

Credit

Hiroki Kumazaki (kumagi), with substantial OpenAI Codex assistance for derivation, coding, separate-agent proof review and independent checker development. Agents share context; implementation independence is not independent human discovery. Apache-2.0.

Credit Philippe Van Velzen and kumagi/PR2353; ywz65/PR2614; Nick Petalas/PR2640 and PR2604; Arham Tahir/PR2675 and PR2682; Sagar Thakrar's mixer handoff; Rohan Arun, Chafik Boukhalfa, Adam Gall, Josie Elliston and Ali Romman for the frozen geometry/native lineage. Douglas Colkitt's ceiling engine retains its Claude assistance credit. No predecessor files changed or vendored.

Open next questions

Before further construction, check whether compatible endpoint-frame assignments or chronology exclude the surviving 406 profile, incorporating stronger local facts from the mixer handoff. TASK.json and the package README give the bounded first step and remaining blockers. This contribution stops after the necessary-constraint audit.