Author

Ibrahim Mian

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Preprint Sep 2026

Kernel-Checked Frontier Certificates for Erd\H{o}s Problem 414

Let $h(n) = n + \tau(n)$, where $\tau$ counts divisors. Erd\H{o}s and Graham asked, after Spiro, whether the orbits of any two positive integers under $h$ eventually share a point (Problem 414 on Bloom's list). The problem is open, and a finite computation cannot close it; nothing about it has been checked by a proof k...

Ibrahim Mian, Shayaan Siddique · 0 citations

Preprint Jul 2026

Machine-Checked Certificates for the Geometric Half of the Minimum Kochen-Specker Bound

The best known lower bound for the minimum Kochen-Specker vector system in $\mathbb{R}^3$ -- 24 vectors -- rests on a computational proof whose combinatorial half emits DRAT proofs but whose geometric half does not: the non-embeddability of thousands of candidate graphs is established by Z3's nonlinear real arithmetic,...

Shayaan Siddique, Ibrahim Mian · 0 citations