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

arXiv:2606.04458v1 Announce Type: new 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 certificate consists of a finite adaptive ledger, a terminal-route replay, three local lower-bound certificate families, compact integrity audits for large tables, and a finite proof-obligation layer connecting the replayed data to the lower-bound statement. Under the stated verification model, acceptance of this finite certificate implies the Brass--Sharifi convex lower bound {\alpha}cvx $\ge$ 0.832. We claim neither a numerical improvement over the Brass--Sharifi bound nor a nonconvex lower bound; proof-assistant formalization and independent external verification remain outside the present scope.