An explicit parameter improvement in Sawin's lower bound for the Erdős unit-distance problem

We optimize the explicit parameter choices in Sawin’s recent lower-bound framework for the Erdős unit-distance problem. Using Sawin’s Proposition 10 and Lemma 12 as black-box inputs, we give a strict Golod–Shafarevich certificate with |T| = 50, |SQ| = 549, and no split primes. A 150-digit interval computation gives δ = 0. 031035468991079569. . . Consequently, within Sawin’s theorem stack, the explicit lower-bound exponent is improved from 1. 014114. . . to 1 + δ = 1. 031035468991079569. . . This record contains the preprint PDF, LaTeX/arXiv source, parameter data, verification scripts, interval certificates, and reproducibility files.