Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Independent review and grade of the matching-window conditional
grade: Independent grade of the matching-prime-gap-window review, including its conditional scope and localized wording refutation.
review: Independent adversarial review of the conditional lattice and matching-window argument, with an actual-prime counterexample to necessary nonzeroness of a finite contribution.
The review examined the full supplied mathematical body of [[research/prime_binary_new_attack/matching_gap_windows|the matching-window conditional]] and the prime-index convention of Problem 251 on 2026-10-16 UTC. The separate grade, examined on the same date, accepts the report and its independence for the explicitly listed surfaces.
The positive conditional results are refutation-failed. The literal assertion that unequal congruent prime-gap windows necessarily contribute a nonzero finite weighted sum is refuted-as-stated. This localized finding does not defeat the matching-window conditional. Within the examined argument, the owning page makes the single body correction authorized by the grade and discloses it. Its added comparison with the step lemma is outside this examination. No prime-pair existence theorem or solution of Problem 251 is accepted.
The subject, submitted review and submitted grade are unchanged copies. They preserve the mathematical argument, all witnesses, the exposure and provenance qualifications, and the separate grading decisions. The review used only the frozen extraction, not the original pages; the grade resolves its attribution from the assignment and exact-copy custody. No mathematical reply was delivered to the reviewer. The disclosed administrative filename exposure was judged immaterial by the grader.
The examination is noncomputational. Its equations and explicit prime and non-prime witnesses are the retained evidence; no executable or repository gate supports the mathematical verdict. The numerical observations elsewhere in this evidence folder are separate and remain at their own standing.
The filed review adds wiki frontmatter, and the filed grade adds a title and wiki-generated metadata. These are the only publication edits; their bodies, scope, dates and verdicts are unchanged. The three submitted snapshots have no edits. No private configuration, message transcript or activity log is part of these public attachments.