A bounded two-tier null result for integer relations on a hybrid Khinchin-K_0 basis, with a structural gap
Year: 2026
Type: preprint
Abstract: A bounded null result on integer relations in a hybrid basis built from Khinchin's constant K_0, its low-order powers, log K_0, and bilinear products of K_0 with seven named constants {pi, e, ln 2, gamma, zeta(2), zeta(3), G}. Sixty-five sub-bases are tested under a two-tier predicate: a rigorous Euclidean-norm bound H_rig = 1.0361 * 10^72 derived from Ferguson-Bailey-Arno 1999 Theorem 1 + Corollary 2 at verification class proven_corollary, and an empirical operational bound H_empop ~ 8 * 10^69 at the primary basis under verification class field_standard_practice per Bailey 1998 section 2's general rule. The M3.1 harness uses mpmath PSLQ with cascading-precision triage (P, 2P, 4P at P = 2160 digits) and an independent PARI/GP lindep second leg. Every sub-basis returns cascade-stable null. The mission also documents a fundamental capability gap at the symbolic-closure stage M4 (K_0's transcendence status is the major open question; seven candidate structural arguments and a four-path SymPy probe each fail), and a Lean 4 statement-shape encoding (~385 lines, Mathlib v4.14.0) which type-checks against an explicit auxiliary-axiom set. The work is conducted under an explicit-evidence-acceptance-and-logging (AEAL) discipline with eleven named heuristics, six audited halt events, and twelve mutation-log entries.
Author: papanokechi, papanokechi
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161404944