Constraint Topology and Regime Formation in Frame-Bound Mechanical Systems

Abstract This work formalizes the structural behavior of Frame-Bound Mechanical Systems (FBMS) through constraint-topology ordering. A regime is defined by a reference structure and an active constraint set. Geometry is treated as the projection of admissible state trajectories rather than as a primary determinant. The framework introduces a Unified Boundary Axiom (UBA), a Constraint–Authority Revalidation Principle (CARP), a Carry-Over Theorem for regime transitions, a dominance-graph extension for distributed systems, and a degeneracy clause for solver-mediated environments. Structural mutation is shown to require boundary crossing in constraint space. Stability is regime-relative and must be revalidated under constraint mutation. The framework is falsifiable and limited to systems whose admissible behavior is constraint-defined.