GLaCS: Grounded Constraint-State Projection for Global-Consistency Reasoning

Global-consistency reasoning requires an answer supported by a joint assignment that satisfies interdependent constraints. We study how to select such an answer from a fixed candidate set. We propose GLaCS, a grounded constraint-state projec- tion framework that separates candidate generation from structured authorization. GLaCS extracts variables and relations from the input and compiles them into executable state computations and factorized consistency scores. Task adapters use constrained assignment search, shared numerical repair, or deterministic execution to score the fixed candidates. The lowest-energy candidate is selected through a shared scoring and intervention interface. On identical reflection self-consistency pools, GLaCS improves accuracy from 0.965 to 0.995 on arithmetic chains and from 0.658 to 0.775 on logic-grid transfer. On four extended BIG-Bench Hard tasks, LLM-extracted graphs yield 0.941 accuracy, compared with 0.711 for an LLM selector given the same graphs. Component interventions, graph perturbations, and stem-only extraction audits characterize the roles of state repair, constraint fidelity, and candidate coverage in these gains.