Carptopus

Tail-projection certificates for cyclotomic minimum-degree polynomials beyond the reciprocal condition

For an odd squarefree integer n=pq_1...q_k with k at least 3, this paper gives an explicit divisor-residue sufficient condition under which the minimum degree of a nonzero nonnegative real multiple of the n-th cyclotomic polynomial is (p-1)q_1...q_k, with equality only for positi...

A Continuous Family of Counterexamples to the Middle Runner Conjecture

The 2015 AIM middle runner conjecture allows arbitrary initial positions and predicts a symmetry between complementary order statistics for runners with commensurable nonzero speeds on a circular track. For velocities (1,2,3) and initial positions (0,0,a), this manuscript determi...

Exact Certificates for the First Two Cases Not Covered by Steinberger's Cyclotomic Minimum-Degree Theorem

Steinberger's cyclotomic minimum-degree theorem leaves 46189 and 96577 as the first two uncovered parameters. This preprint proves the conjectured minimum degree and unique monic nonnegative-real minimizer for both values using exact integer separation certificates in a CRT tenso...