When the Manifold Collapses: A Geometric Theory of Constraint Conflict in Large Language Models

Mabrok 2026 proved that the expressibility gap of LLM hidden-state manifolds obeys a linear volume scaling law under regularity conditions including a positive mar- gingradientlowerbound. Weprovethatthisregularityfailsundercontextualconstraint conflict. Using the Riemannian coarea formula, we show that when the empirical coarea density becomes singular near the Voronoi boundary — AC(s)∼s−α with α>0 — the linear scaling η(ε)∼ε transitions to a sub-linear power law η(ε)∼ε1−α (Theorem 1). We prove that constraint conflict induces Fisher metric degeneration along margin- relevant directions, with Fisher sensitivity bounded by O(1/K) when probability mass diffuses across K competing alternatives (Theorem 2). Experiments on six transformer architectures (124M–1.5B parameters) across five constraint conflict levels confirm the theory: three of six models exhibit statistically significant scaling collapse under ex- treme conflict (β <1 with 95% bootstrap CI excluding 1), and five of six show at least one collapse cell across the five levels (8 of 30 cells total), with the strongest deviation at β = 0.667 0.595,0.743 for OPT-1.3B. Fisher boundary distance contracts fivefold and Fisher metric eigenvalues contract by 50% under strong conflict. We propose a three- phase classification of manifold response to constraint conflict: Navigation (connected, enriching), Collapse (degenerate), and Fragmentation (disconnected, hallucinatory).