Rigidity, Monodromy, and Recursive Enumerability: A Unified Framework for Interpretive Stability with Empirical Calibration, RCE Protocol Design, and Cross-Domain Transfer

We present a unified categorical framework linking interpretive dynamics in large language models, rhetorical commutativity in Foundational Commutative Rhetorical Mechanics (FCRM), and rigidity phenomena in computability theory. The central insight is that ambiguity is monodromy and rigidity is trivial π₁. We provide: (1) a rigorous fibration model of LLM interpretation with explicit cleavage constructions; (2) an axiomatization of the Rigidity Constraint within FCRM, proving that RCE commutativity induces functorial cleavages; (3) an empirical calibration method defining a monodromy metric for prompt variance; (4) a Rust implementation of an RCE protocol that provably induces contractible base subdomains; and (5) cross-domain transfer results applying condensed-mathematics techniques to complexity classes and logical strengths. All results are mechanizable in HoTT/Coq or Lean. This work establishes the Rigidity Constraint as a universal principle for interpretive stability across semantic, rhetorical, and computational domains.