3 papers
cs.LO2026
A Kernel-Checked Exclusion Certificate for Erdős Problem 647
Ibrahim Mian, Shayaan Siddique
Erdős problem 647 asks whether any satisfies , where is the divisor-count function. Computational searches have excluded solutions up t…
cs.LO2026
Machine-Checked Certificates for the Geometric Half of the Minimum Kochen-Specker Bound
Shayaan Siddique, Ibrahim Mian
The best known lower bound for the minimum Kochen-Specker vector system in -- 24 vectors -- rests on a computational proof whose combinatorial half emits DRAT proofs…
cs.LO2026
Kernel-Checked Exclusions for the Erdős-Selfridge Odd Covering Problem: Any Odd Covering of Has lcm Exceeding 10000
Ibrahim Mian, Shayaan Siddique
The Erdős-Selfridge odd covering problem (Erdős problem #7) asks whether a covering system of exists whose moduli are all odd, distinct, and greater than 1. The proble…