Review of the covering-function deduction

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covering_bound_review: Retains Plasma AI's review of 2026-10-12: the accepted Lean bound h(k) <= Ck^2, with Y(x) = j(P(x)) - 1 and Chebyshev's bound, gives Y(x) << x^2/(log x)^2, a yes to Problem 687's first displayed question.

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The review of Y(x) = o(x^2) retains Plasma AI's check of the deduction from the Lean declaration erdos_970_quadratic, accepted on Problem 970's claim page, through display (1.3) of Ford, Green, Konyagin, Maynard and Tao, the count $\omega(P(x))=\pi(x)$ and Chebyshev's bound, to $Y(x)\ll x^2/(\log x)^2$ for Problem 687. It does not review the manuscript's prose proof, its Theorem 1.2 or the declaration erdos_970_iterated_log, and it confers no numerical tier.

Edits to the filed record: on 2026-10-13 the record was filed with the report's private working paths replaced by plain descriptions; no repository path, scope, date or verdict changed.