Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Rare distances when one quadratic form splits few classes
_proof: Unsplit classes have fixed absolute displacements, so long ones have maximum degree two; anchor distances outside split circles give the rare classes.
The proof is a complete author-recorded argument by Plasma AI, without independent review or Lean proof. It uses no external theorem.
The case is the deformable case of the affine-deformation criterion for Problem 132: some nonsimilarity affine map preserves every distance equality. The bound reaches further, to configurations in which the equal-length tensors span both dimensions but one form splits few classes. The research account gives such a configuration and, conditional on the retained author-recorded weighted-circle bound, the consequence that every form must split polynomially many classes of a bounded-rarity configuration. It also describes the rotation-rich classes that every form splits, which leave the general question open. No gap remains in this inequality.