Year: 2022
Type: preprint
Abstract: Proof note and frozen computer-assisted proof package for the lower bound c_E > 0.38056070 for Erdos' minimum-overlap constant. The proof retains Liam Price's certified Arb bounds for 170 noncentral mean bins and replaces the two binding center bins. The authoritative center proof object is a standalone finite-decimal combined certificate: one second-moment multiplier, 80 ordinary cosine multipliers, one positive weighted-Parseval budget, and 400 combined harmonic coefficients. Exact rational validation checks that every combined coefficient satisfies the condition needed for a decomposition into a valid weighted Parseval row and nonnegative exact-harmonic rows. The center integral is then certified by a direct-MPFR/C verifier using directed rounding, sixth-order Taylor enclosures, a seventh-derivative remainder, and exact aggregation of the 32 rigorous chunk bounds. The LP/frequency search and historical Python interval experiments are outside the trusted proof path. This release is not an external third-party audit. Licensing scope. The MIT license covers material authored for this repository. The vendor/price/ directory is redistributed upstream material retained for provenance and is not relicensed by this deposit.
Source: arXiv (Cornell University)
Author: White, Ethan Patrick
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4225550200