Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Discrete geometry
L143_split_class_rarity/: If some traceless quadratic form takes unequal values on equal-length pairs in only kappa distance classes, at least (n-1-2 kappa (M+2))/4 distances occur at most n times.
L28_cube_refinement_threshold/: A residue-path argument and an elementary odd-dimensional gcd bound give an explicit threshold for every larger cube count.
L29_repeated_distance_counting/: Two counting inequalities isolate the isosceles-triple contribution missed by a disjoint-pair distance-energy estimate.
L30_nine_point_distance_rigidity/: An exact nonsingular fourteen-variable Jacobian excludes nearby eight-distance repairs of one configuration with forbidden degeneracies.
L32_equilateral_witness_size/: A strip coloring and compactness of bounded connected configurations force any two-scale non-two-colorability witness to grow near scale ratio one.
Each claim states its hypotheses, conclusion and evidence standing. The cube-dissection and coloring arguments are elementary proofs; the local distance-rigidity claim also retains exact executable evidence.