Solver-Hard Is Not Model-Hard: A Hardness-Controlled Diagnostic for LLM Constraint Reasoning

תקציר מקורי באנגליתarXiv:2607.17047v1 Announce Type: new Abstract: LLM constraint reasoners are often evaluated near the random-SAT phase transition, confounding density and solver hardness. We test instance-level transfer while near-matching clause density. At aligned size bins, with near-matched density and matched maximum clause width, we compare proof-hard expander-Tseitin and proof-easy ladder-Tseitin formulas, pigeonhole anchors, and density-mismatched controls. Theory separates their resolution hardness; a solver-specific Glucose mean-conflict proxy differs by up to $51\times$, and five other solvers preserve the direction. Across three included models (243 instances each; a fourth is excluded for abstention), the near-matched-density accuracy gaps range from $-32$ to $+20$ points, with a pooled gap o