A negative, inconclusive search for further shifted lonely runner covers at n = 39..94 (companion to n = 63)
Year: 2026
Type: article
Abstract: Computational negative-result note (Tier X; nothing new is claimed). After the exact shifted lonely runner counterexample at n = 63 (doi 10.5281/zenodo.24051700) we searched for a second n in 39..94 using bases not used there: multiples of 3, 4 and 6 and wider even pools, with shift menus c/q + j/D (q in 4, 6, 8, 12), exact CP-SAT set cover and two exact checkers. No cover was found. Controls: n = 63 and n = 95 are re-found (both checkers COVERED) and n = 44 is INFEASIBLE in the control family. Decided verdicts: the narrow-menu family (q = 8, offsets |j| ≤ 4) is INFEASIBLE for n = 39..93 except n = 81 (UNKNOWN), but it also fails the n = 63 positive control, so it is evidence only about that narrow menu; the wide-menu (|j| = 8) and multiple-of-3/4/6 families are UNKNOWN at 45-90 s (solver-limited, uninformative). About 9.6 of a 12 core-hour kill budget was used, so the preregistered kill rule was not reached. This does not show that no other n exists; it is not evidence about the (unshifted) lonely runner conjecture. Producer is an AI agent; no independent audit, no Lean, no human review. Code, per-run logs (logs/runs.jsonl), control certificates and SHA-256 manifest are in the bundle.
Author: Callens, Xavier
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225771746