A publicly checkable lower bound on B (Erdős problem #513): slack-free interval-arithmetic certificates, and, to our knowledge, the first independent verification of the Sothanaphan frontier certificate

Certified lower bound B >= 0.5850788196 for the maximum-term vs maximum-modulus ratio constant B (Erdős problem #513) from a fully specified entire function, by a slack-free dyadic root-cover certificate in 50-digit interval arithmetic (12-second replay), together with, to our knowledge, the first independent verification of the frontier certificate B >= 0.585078819653 (Sothanaphan progress note, 2026-02-27, AI-generated; no prior third-party verification found: problem page, forum, tracker changelog, AI-contributions wiki, web searches, 2026-08-01): from-the-math re-implementation (identical node counts), reproduction of the public code (mpmath >= 1.4 compatibility defect documented and patched), and a method-independent mesh+Lipschitz cross-check. All claimed numbers are machine-checkable from the bundled scripts and logs. Production chain: AI-assisted search and code, machine-checked certificates, human-prepared exposition.