6 papers
A Machine-Checked Proof that Gardam's Lattice Does Not Have Unique Products
Ibrahim Mian, Shayaan Siddique
Kaplansky's zero-divisor conjecture asserts that the group ring of a torsion-free group over a field has no zero divisors. It holds for every group with the unique-product property…
Kernel-Checked Frontier Certificates for Erdős Problem 414
Ibrahim Mian, Shayaan Siddique
Let , where counts divisors. Erdős and Graham asked, after Spiro, whether the orbits of any two positive integers under eventually share a point (Problem 4…
A Kernel-Certified Verification of the Erdős-Mollin-Walsh Conjecture below
Ibrahim Mian, Shayaan Siddique
Erdős problem 364 asks whether three consecutive powerful numbers exist, where is powerful if implies . Erdős (1976) and, independently, Mollin and Walsh…
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…
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…
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…