Reviews and grade of the Problem 49 reconstructions

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grade: Distinct grader's record for the six focused reviews of the Problem 49 reconstruction pages as they stood on 2026-09-28T05:03:27Z: all six reports pass, five corrections are accepted (three from required findings, two promoted from suggested ones on the grader's own verification), every page is graded on fidelity and argument, and no tier is assigned.

lemma_3_2_reconstruction_review: Refutation-failed review of the Lemma 3.2 reconstruction: the statement, locators and citations match the source and the argument is sound, with one required correction (the desc widens "natural numbers j" to "integers j").

lemma_4_1_reconstruction_review: Faithful with corrections: the statement, the candidate set and every locator match the source, but the written-out proof of (iii) asserts a lower bound for the largest prime factor that its stated justification does not give; one required correction, the conclusion survives.

lemma_5_1_reconstruction_review: Refutation-style review of the Lemma 5.1 reconstruction against p. 9 of the held manuscript: source fidelity faithful and the argument sound as written, with no required corrections, two suggested corrections and three notes.

theorem_1_2_reconstruction_review: Fresh-context refutation review of the Theorem 1.2 reconstruction as it stood on 2026-09-28T05:03:27Z: the statement is faithful to the source and the reconstructed argument is sound given its imported inputs; zero required corrections, two suggested corrections and three notes.

theorem_3_1_reconstruction_review: Faithful with one required correction: the page turns the source's "we can assume" into a universal statement about P_1(x;k) that fails for n=4, k=2; the one deduction the page reconstructs is sound.

theorem_3_3_reconstruction_review: Fresh-context refutation attempt on the Theorem 3.3 reconstruction: the statement is faithful to the source and the argument is sound as reconstructed, with no required corrections, two suggested wording corrections and two notes.

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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 per page for Lemma 3.2, Lemma 4.1, Lemma 5.1, Theorem 1.2, Theorem 3.1 and Theorem 3.3, each by a reviewer in a fresh context under a refutation charge against the held author manuscript of Pollack, Pomerance and Treviño (2013), and one distinct grade by a grader distinct from the author and from every reviewer. All six reports pass; the grade accepts five corrections (C1--C5: a desc domain, one sentence of the Theorem 3.1 sketch, the index $i=0$ in the proof of Lemma 4.1 (iii), and two scope sentences) and records every page as faithful to the source, with the arguments sound as reconstructed given their labeled imports. These are focused reviews: they assign no tier, change no status, and leave the pages author-recorded.