Alman and Vassilevska Williams (arXiv:2610.06783) gave the first polynomial improvements over the textbook algorithms for 3SUM and APSP: deterministic algorithms with exponents 1.9992 for 3SUM, 2.9983 for Exact Triangle and 2.99942 for APSP. Their algorithm has two steps: a matrix theorem, computing N^2/sqrt(D) prescribed entries of the product of an N x D and a D x N integer matrix in time N^2/D^gamma, gamma > 0, when D <= N^eps, for every eps < 0.1204; and reductions from the three problems to the lopsided sparse triangle problem. We improve both. With Schönhage's five-term partial-product tensor, the matrix theorem holds for every eps < 0.172. The preprint's reductions keep a quarter of the matrix theorem's saving for 3SUM and a half for Exact Triangle and APSP; ours keep all of it, by calling the counting version of the triangle problem adaptively and building composite moduli one prime at a time. Together this gives deterministic 3SUM in n^{1.9945+o(1)}, and Exact Triangle, (min,+)-product and APSP in n^{2.9945+o(1)}. We also improve on the preprint's proof sketch for 3XOR and solve it deterministically in O(n^{1.99451}). Which other problems on three lists does the method make truly subquadratic? It solves 3SUM over F_p^d for every fixed prime p with 3XOR's exponents, and over every finite abelian group of exponent p^2, such as Z_4^d, in O(n^{1.99726}). For coordinatewise problems with a fixed relation P on every coordinate triple, a certified exhaustive computation shows that every Boolean P, and every functional P over three letters, either is the solution set of an equation over Z, F_2 or F_3, and the problem is then truly subquadratic, or has a gadget for Orthogonal Vectors, and the problem is then hard under the Orthogonal Vectors hypothesis. Over four letters, just four functional relations, up to symmetry, satisfy neither condition.

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