[petalas]

Summary

Exclude the four-six-cycle fifteen-owner equality graph from the historical calls-0/4 centre route and coefficient model. Claim type: scoped written proof conditional on the cited route, column-completion and graph-classification premises, with exact finite corroboration. No new kappa.

connected cycle boundaries force c0 = c1 = c2 = c3
B3-D0 and B3-D7 then repeat the same incident port

Krzysztof Wójt's merged #5239 classifies the nonzero-six-cycle equality branch. dcharb78's #3147, exact head 5cbc48b18cb05327a8dacab3f626412d3bc5e924, supplies unique dependent-triple completion. Those are cited inputs. The new contribution is their forced-label consequence for this graph, produced by Nick Petalas. Credit Sagar Thakrar #3291, Nick Petalas #5182, Matarener #3656 and the retained centre-query lineage.

Evidence

• Before: the abstract equality classification retained the four-six-cycle graph as a possible route-realization branch. After: its external-edge constraints force two equal labels at B3, contradicting distinct incident ports. The fifteen-owner support floor remains unchanged.
• The standalone verifier checks the named cycle boundaries and their connected auxiliary square. All 256 assignments of four colors to the four cycle labels give four assignments obeying the cycle links and zero with distinct ports at B3. Four colors cover every equality pattern on four labels. A positive separated-leaf cycle, two rejection controls and three part-preserving relabelings pass.
• Both registered warning-strict normal and optimized commands passed locally, each timed at 0.01 seconds. PASS_FIFTEEN_OWNER_CYCLE_ROUTE_OBSTRUCTION assignments=256 legal=0 collision=B3 and PASS_REGISTERED_RESEARCH_PACKAGE were emitted.
• Committed bytes and source history passed at 2ba6c502f57ae25728c322c402f80e844805c55c, covering seven package/input files. Export integrity and both read-only, Git-free exported runs with an empty PATH passed. The replay reads only the cited graph and prints generated file-hash receipts.

Reproduce from the repository root with the available interpreter, or substitute another absolute CPython 3.12 path:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/fifteen-owner-cycle-route-obstruction/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/fifteen-owner-cycle-route-obstruction/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/fifteen-owner-cycle-route-obstruction
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/fifteen-owner-cycle-route-obstruction --check-source-history

Local environment: CPython 3.12.15, macOS 27.0.1 arm64, standard library only. Sparse checkouts need this package and research/centre-equality-six-cycles/WITNESS.json.

Limitations

The six-cycle-free fifteen-owner branch remains open. The corollary inherits the cited source premises, including the pending unique-completion statement. The registered replay does not validate predecessor results. No larger support exclusion, physical supplier, paid-profile improvement, selected-frontier change or complete multiplication theorem is claimed. All five selected framework assumptions remain. Independent human and formal proof-kernel review, the selected cold replay, Lean and Docker are unrun. No required local check is deferred to CI.

Main and merged-result searches, 748 open PRs, a subsequent 100-PR update check and current local claims were screened for overlap. The latest successful Discussion snapshot was 2026-11-06 13:44 UTC; the later Discussion refresh was rate-limited. Unpublished work and arbitrary historical diffs remain outside that coverage. Advance CLAIM.

Open next questions

1. Can a six-cycle-free fifteen-owner equality graph carry the actual routes and nonzero coefficients? Start with the duad/perfect-matching example and impose its eight-cycle route equations. No labeling or coefficient solution is supplied here.
2. Can external-label propagation exclude a larger graph with connected six-cycle components? First bind its cubic cycle vertices and external edges. Higher-degree vertices need another coefficient argument.

Related open work

• #3147 studies the same historical centre-repair model and asks about labelled braid incidence beyond twelve owners. Its unique-completion property is credited as a premise; this PR excludes the specific four-six-cycle fifteen-owner branch supplied later by Classify fifteen-owner equality graphs with six-cycles (no new κ) #5239. No predecessor numerical result is rechecked or claimed as new.

The completion refresh inspected the nine other account open PRs created since the advance CLAIM at 2026-11-06 13:44:22 UTC, PRs #6795 through #6803. None studies the fifteen-owner route graph or computes the same quantity. No additional related entry or numerical comparison was needed.

CI notes

Both hosted checks passed at exact head 2ba6c502f57ae25728c322c402f80e844805c55c in run 42229748582: plan and registered package replay.

The completed check list was read once. Hosted replay executed the registered normal and optimized finite checks. The local package, committed-byte/source-history and read-only export checks also passed. CI success certifies execution of these checks; the cited mathematical premises and full multiplier obligations remain inherited. Independent human and formal proof-kernel acceptance are unclaimed.

Merge Danger

Door: two-way. Blast radius: one isolated opt-in research package.