Heuristic Mime Theory: Constraint Illusions, Simulated Rigor, and the Geometry of Performative Abstraction

This manuscript introduces Heuristic Mime Theory (HMT), a rigorous operator-theoretic framework that models the emergence of simulated rigor in intellectual, academic, and institutional discourse. Frequently, complex systems of thought maintain aesthetic formalism, technical vocabulary, and unearned confidence without actually defining the operators required for coherent logical transport. We define this phenomenon as "heuristic mime behavior"—the act of gesturing at invisible structural constraints without interacting with admissible mathematical or conceptual architecture. Through this framework, the manuscript formalizes the strict boundary between genuine derivational coherence and performative abstraction. It derives quantitative measures for semantic instability, introducing metrics such as "Definitional Density," "Gestural Amplitude," and the "Hand-Waving Functional." Furthermore, it proves the inevitability of mime-phase transitions under operator incompleteness, culminating in the Nontrivial Mimetic Collapse Theorem. By providing empirical diagnostics for detecting theatrical abstraction cascades, this work serves as a formal tool for identifying when symbolic motion ceases to transport actual intellectual mass. Complete appendices provide admissibility proofs, operator closure theorems, semantic entropy bounds, and finite-time hand-waving blow-up conditions. Ultimately, this manuscript serves as a formal mathematical mandate: Define the operator. Terminate the mime.