Independent research · Austin
Solvable targets compile by class field theory. Screening polynomial families was saturated at the frontier.
Jonathan Washburn
Results as of 6 July 2026 · early note, kept as dated
Abstract, as written in July
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.
This note is kept because the measurement still stands: screening parametric families, at the frontier that existed in early July, produced volume and no new cells. The compilation picture for solvable layers also still stands. What the later work added, and what this note does not contain, is the sibling coordinate: the square class in the orbit field, and the single linear system that names a cell before the polynomial exists.
Read the discoveries and the longer argument for the mathematics as of 16 August 2026. Do not take the July counts as the closing state of the board.