Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Whole-statement examination and grade
grade: Independent PASS grades for the unchanged one-sided review and its four assigned conclusions, with separate mathematical and independence findings.
grading_derivations: Mathematical checks used to grade the unchanged one-sided report, including the transport, planar bound, localization and separate extrema.
report: Whole-statement adversarial examination of the two supplied all-sequence one-sided discrepancy bounds and their separate extremal consequences.
review_derivations: Independent derivations and exact attempted refutations of the supplied one-sided circle discrepancy argument.
The whole-statement report and its distinct grade, examined on 2026-10-15 UTC, cover both one-sided sequence bounds and, separately, each extremal inequality and its integer- divergence. The grade is PASS, and the mathematical verdict is refutation-failed. Both roles disclosed GPT-6 Astra and worked in separate fresh, isolated contexts, distinct from authorship and each other. The grade supplies the tier-1 warrant recorded on the native claim.
The subject manifest names the exact frozen extracts and their original source ranges. The mathematical freeze is 2026-10-15 at 09:49:19.072889 UTC. The submitted report and grade are retained with their mathematical inputs and supporting derivations. No mathematical software or missing private witness is needed to reconstruct this analytic assessment.
Scope and independence qualifications
The reviewer and grader checked the complete supplied local deductions. The original source publications were unread; supplied attribution is preserved without claiming independent original-paper fidelity. Korsky's cited preprint remains unrefereed. No native claim or unprovided external theorem is consumed as an established premise. No Lean or computational warrant is asserted.
The private inbox could not be inspected and is unread, not established empty. The grader evaluated the complete available received-input and action records and found no excluded content consumed. Opaque internal fields were retained but not decoded. The full grade states these access limits and its own eligibility ruling; neither empty subscriptions nor a preparer's waiver replaces that ruling.
The grade controls the report's historical communication assertion. Its blanket sentence that no messages were read is not literally accepted: the reviewer later read its own authorized sent receipt, after completing the mathematical report. The grader's explicit content-based ruling finds this own-output confirmation immaterial. The unchanged report and the full ruling remain available together. No incoming message or excluded communication was identified as consumed.
The ratio inequality, the literal original first two expressions, equality of distinct-point and unrestricted extrema, optimal constants and attainment are outside this record. The planar proof and both anchored conventions are inside its scope; no unread original paper substitutes for that proof.
Canonical correspondence and editorial treatment
On 2026-10-15 the integrator compared every ranged mathematical payload with its canonical source selection. They agree exactly after the extraction's stated cuts and removal of the author-standing labels. The prepared provenance map is a source account, not a canonical-page extract. The native claim states the same examined assertion. Its proof gives a concise navigation and composition account of the unchanged supporting deductions; the exact examined proof remains in the snapshots. This correspondence work is not another independent examination.
The readable report, grade and derivations retain their mathematical text, verdicts, dates and qualifications. Wiki metadata, separators and maintained relative links are added. The original submitted report, grade and derivations are retained unchanged under assets, including their original relative layout. In the subject manifest only the private mathematical-source revision and per-file hashes are removed under convention 9; source paths, selection ranges, freeze time and scope remain. No report is represented as having examined a later substantive repair.
The whole-conclusion and exact-formulation assessment for the conjunction of the ratio and one-sided results is a separate obligation. This record does not itself accept Problem 1221 as solved.