Reviews and grade of the Problem 15 reconstructions

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grade: Distinct grader's record for the four focused reviews of the Problem 15 reconstruction pages as they stood on 2026-09-28T05:03:27Z: all four reports pass, seven corrections are accepted (the regime of display (3.8) and the scope of Lemma 3.2, a tiling slip, a misattributed justification and two consumer interfaces on the Theorem 1.4 page, and one fidelity sentence on each of the other two pages), the pages are graded faithful with corrections and sound, and no tier is assigned.

lemma_3_1_reconstruction_review: Focused refutation-charge review of the Lemma 3.1 reconstruction as it stood on 2026-09-28T05:03:27Z: the statement is faithful to the source and the argument is sound, with no required corrections, one suggested wording change and two notes.

lemma_3_2_reconstruction_review: Focused independent review of the Lemma 3.2 reconstruction against the held arXiv v3 PDF: faithful with corrections, with two required corrections (the regime condition on display (3.8) and the missing largeness hypothesis on d in the statement), one suggested correction and three notes.

relation_2_1_reconstruction_review: Fresh-context refutation review of the relation (2.1) reconstruction: the statement is faithful to the source and the reconstructed argument is sound, with zero required corrections, one suggested labeling change and three notes.

theorem_1_4_reconstruction_review: Fresh-context refutation review of the Theorem 1.4 reconstruction as it stood on 2026-09-28T05:03:27Z: source fidelity faithful with corrections and the reconstructed conditional argument sound, with one required correction, a misattributed justification in the Step 8 remark on the indexing of the recursion.

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The records here are the independent focused reviews of each reconstruction page of the folder as it stood on 2026-09-28T05:03:27Z, one for the Lemma 3.1 page (review), one for the Lemma 3.2 page (review), one for the relation (2.1) page (review) and one for the Theorem 1.4 page (review), each by a reviewer in a fresh context under a refutation charge against the held PDF of Tao (2023), and one distinct grade by a grader distinct from the author and from all four reviewers. All four reports pass; the grade accepts seven corrections (C1--C7), two of them to the regime of display (3.8) and the scope of Lemma 3.2 on the Lemma 3.2 page, and records every page as faithful with corrections and sound, the Theorem 1.4 page conditionally on Conjecture 1.3. These are focused reviews: they assign no tier, change no status, and leave the pages author-recorded.