A Reproducible Certificate for the Brass$-$Sharifi Lower Bound in Lebesgue's Universal Cover Problem

arXiv:2606.04458v2 Announce Type: replace Abstract: Brass and Sharifi proved the lower bound 0.832 for the convex form of Lebesgue's universal cover problem by combining geometric estimates with a computer search over placements of a disk, an equilateral triangle, and a regular pentagon. This paper gives a certificate-based reproduction of that computation. The finite record consists of an adaptive ledger, a terminal-route replay, three local lower-bound certificate families, compact integrity audits for large tables, and a proof-obligation layer connecting the replayed data to the lower-bound statement. Under the specified verifier, acceptance of the finite certificate implies the Brass$-$Sharifi convex lower bound $\alpha_{cvx} \ge 0.832$. The certificate concerns only the convex Brass$-$Sharifi lower bound statement: it claims neither a numerical improvement nor a lower bound for the unrestricted nonconvex problem, and proof-assistant formalization and independent external verification remain outside the present scope.