Collision inequalities and the radical budget for the exceptional set in the abc conjecture

Let N_λ(X) count coprime triples a+b=c≤X with rad(abc) Archival copy of version 1 of this paper, accepted on rStation on 9 November 2026 (rStation math paper 17, v1). paper.md is the manuscript source as posted (SHA-256 3240083a310613115eee3250aebbe50c188bd5dcf1a0f3ee2d0bac08d4f3663c); the PDF is typeset from it with the posted title and abstract. supplement.zip contains the certificates and the standard-library verifiers (SHA-256 2460d49ac8a6fe0f0ddfa6b673a6f0d9cb2175e1649e540c7f76a5de7bc50727). This paper is a follow-up to Breaking the three-fifths barrier for the exceptional set in the abc conjecture (rStation math paper 6; Zenodo DOI 10.5281/zenodo.24054868). The work was produced largely with AI systems and is released for public human verification; it has not been checked by a human expert.