Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Independent examination and grade
order_26_examination: Whole-conclusion adversarial examination of the frozen order-26 argument, with an independent exact derivation of its compact table, full evidence replay, failure-exit probes, scope qualifications, and dependency findings.
order_26_grade: Scoped pass and void judgments on the complete frozen examination, its independence and replay evidence, with the support and metadata limitations preserved and independently checked.
The whole-claim examination and its distinct passing grade, dated 2026-10-14, support the refutation-failed verdict for every finite simple bipartite graph of order at most 26 being four-choosable and for . Both disclosed GPT-6 Astra and fresh, isolated contexts; neither the examiner nor the grader authored the subject. The grade is the acceptance warrant recorded by L78, not a new assertion by the filing integrator.
The grade rules explicitly on the disclosed preparation-concurrency breach: it does not void mathematical independence on the supplied content evidence, but full concurrency compliance is not certified. The grade also retains two mathematical/runtime qualifications. Support on subsets meeting both fixed lists is sufficient, not universally necessary; adding unit mass at the empty set preserves a strict contradiction. The retained side counts are integers, but value-equivalent floating-point counts can pass the validator. Neither qualification refutes the theorem.
The frozen subject manifest
identifies every original path and the extraction date. The original
statement, proof, source and inputs are kept under
../assets/review_subject/. The reports and runnable checks retain their
mathematical content; only wiki frontmatter and navigation are normalized
for filing. The canonical proof's closing support discussion states the
grade's sufficiency qualification, and the examined wording remains in
the frozen proof. No inspected theorem statement, certificate or checker
is replaced by that clarification.
The original failure-exit keeper checks actual failure behavior in ordinary and optimized Python. The direct arithmetic check independently counts palette subsets and has an explicit negative mutation. The grading replay adapter uses the unchanged retained evidence harness; it is an adapted infrastructure replay, not full initialization of the repository's tools package. Complete commands and limits are in the reports. The paper calculation and analytic reduction remain essential: successful finite execution alone does not establish the universal graph statement.
The exact value of , a solution for general , novelty, optimizer certification and formal verification are outside this acceptance.