Exceptional-width examination and grade

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grade: Independent grade of the frozen omega exceptional-width examination, with separate decisions on the construction, the formulation-remark gap, and the unused strict-zero source clause.

report: Independent examination of the exceptional-width counterexample for omega, including density, real endpoints, external premises, and the limits of its formulation remarks.

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The report and separate grade, both dated 2026-10-14, accept the whole density-one width construction with verdict refutation-failed. The reviewer and distinct grader each disclosed GPT-6 Astra and worked in fresh, isolated contexts. Their work is credited to Plasma AI. The grade warrants the tier recorded on L34.

The subject manifest identifies the five snapshots frozen at 2026-10-14T17:27:31.684793Z. The canonical proof preserves their core construction and omits the literal stronger-width assertion at lines 104–106 of the argument snapshot. That assertion has the separately accepted verdict proof defective; statement unresolved: failure of everywhere $o(\log\log n)$ for this particular width requires infinitude of its exceptional set, which is not proved. This missing assertion is not a premise of the accepted construction.

The report also gives the accepted refuted-as-stated witness $x=2,m=1,h=0,f\equiv0$ for the unused universal strict wording of the supplied EPS97 lemma. It does not refute or independently prove the positive-$K$ specialization consumed by L34. The source proof and page images were outside this examination; its source interface was checked from the supplied statements. Euler's divergence is also an explicit external premise.

The report, grade and all snapshots retain their delivered mathematical text unchanged. Wiki metadata and generated navigation are the only publication additions. The grade supplies the supplemental original-path mapping for the source-depth paragraph that the reviewer's manifest did not identify. The historical-record limits remain in the grade; no complete interaction history is certified. All mathematical reasoning and exact witnesses are retained in prose, with no executable required.