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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

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Verification of the two-tree and star-sharpness unit

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proof_chain_review: Retains the review of the marked-cut count, both lemmas, the rooted word bound, Theorem 1 and the tree Ramsey corollary, with the E0548, E0547 and E0557 verdicts.

proof_chain_review_fresh: Fresh-context refutation-charge review of the six written proof pages (marked count, Lemmas 1 and 2, rooted word bound, Theorem 1, tree Ramsey corollary) as they stood on 2026-09-18T07:24:04Z: refutation-failed.

proof_chain_review_grade_fresh: The distinct grader's report-contract and independence assessment of the fresh six-page proof-chain review as of 2026-09-18T07:24:04Z: PASS and PASS, with the grader's own rederivations and the exposure rulings recorded.

two_tree_grade: Preserves the distinct grade, independent rederivations, withdrawn link finding, exact documentary corrections and bounded acceptance conditions.

two_tree_review: Preserves the whole-unit review, complete deductions and attacks, and documentary findings for the two-tree bound and two-color star sharpness.

two_tree_source_reading: Pins the exact two-page review subject and its source interface, preserves the separate reading scopes, and maps historical findings to the rendition.


The independent review concerns the exact original two-tree bound and star-sharpness subjects. The distinct grade preserves its independent derivations, all findings and the withdrawn link correction. The source-reading record pins the two historical assets, separates every reader's scope, and maps the documentary corrections and three added smaller-host clauses to the current result pages. The separate proof-chain review retains the earlier review of the six original proof pages and the Problem 548, 547 and 557 deductions; on 2026-09-18 a materiality grader ruled its exposure material, so its PASS is void as independent acceptance and it stands as a collaborator-side check whose lemma_1.md repair remains recorded. The fresh proof-chain review, by a fresh-context blind reviewer (model: Claude Fable 5.1) distinct from the earlier reviewer, read the six proof pages and the PDF as they stood on 2026-09-18T07:24:04Z and returned refutation-failed; its distinct grade, by a grader (model: Claude Fable 5.1) distinct from the reviewer, records PASS for the report contract and PASS for independence and accepts that review as the independent proof-coverage review of the six-page reconstruction. The problem pages' own deduction paragraphs were outside the fresh subject.

The review and grade are premise-relative to the sharp tree-free edge bound at its recorded standing. They do not repeat the source proof-chain or PDF review, extend sharpness to general numbers of colors, or supply formal, execution, native-tier or catalog-status credit. The native rendition passed fidelity review and hand check before it was filed.