Holonomic Constraint Geometry as a Computational and Cryptographic Resource

This work develops a geometric framework in which non‑local correlation structures—typically associated with quantum entanglement—arise from holonomic constraints imposed on an extended configuration space. By modeling systems through relations of the form \( g(q1, q2, ..., q_n) = 0 \), we show that non‑factorizable joint statistics, contextuality, and instantaneous global consistency emerge as purely geometric consequences of constraint manifolds rather than dynamical or causal interactions. The approach establishes a structural isomorphism between classical angle‑sum constraints (e.g., triangle geometry) and entanglement‑phase constraints, demonstrating that both systems exhibit reduced degrees of freedom, global coupling, and no‑signaling behavior. Building on this foundation, the paper explores computational and cryptographic applications, including correlated randomness, geometric one‑way functions, constraint‑synchronized distributed systems, and quantum‑inspired algorithms. The framework provides a novel interpretation of entanglement as geometric non‑separability and opens new avenues for constraint‑based information processing.