Independent research · Austin
A 6 July 2026 comparison of polynomial screening and class-field construction for solvable targets. The measurements concern the stated search frontier; the construction argument concerns solvable groups.
Jonathan Washburn
Measurements: 6 July 2026
Abstract
The IGP24 competition asks teams to realize as many of the 25,000 transitive permutation groups of degree 24 as possible by monic irreducible integer polynomials, scored per (group, signature) pair, with 165,836 pairs abstractly allowed. A four-hour sweep producing 289,330 verified hits from a quadratic-tower family yielded zero pairs new to the public grid. A controlled eight-arm GPU comparison across 72 GPUs produced no new pair in any arm. For solvable targets the problem is not a search but a compilation: class field theory constructs each abelian layer of a subnormal series with a prescribed conductor, the conductor-discriminant formula makes discriminant cost a linear objective over conductor exponents, and the archimedean signature is governed by the base field’s conjugation structure and the 2-primary layers. A pilot compiler certified nine (group, signature) pairs then undiscovered by any of the five competing teams, including both extreme signatures of 24T1, 24T2, 24T3 realized directly over ℚ and a depth-2 realization of 24T81.
The measured sweeps found no new cells at the July frontier despite producing many verified polynomials. Class field theory offers a construction route for solvable layers. A related question concerns the sibling coordinate: the square class in the orbit field and the linear system that names a cell before the polynomial exists.
Read the discoveries and the mathematical account for the classification and construction results. The counts here describe the measured July sweeps.