Rigor Deficit and Symbolic Theatricality in Modern Technical Discourse: Toward an Operator-Theoretic Epistemology of Derivational Integrity

This manuscript constructs a formal, operator-theoretic framework for analyzing the growing divergence between actual derivational rigor and performative abstraction in modern technical discourse. As fields like artificial intelligence, quantitative finance, and theoretical physics grow increasingly complex, a phenomenon termed "symbolic theatricality" emerges: the escalation of symbolic sophistication and jargon without a proportional grounding in semantic or mathematical closure. The framework models technical discourse as a directed dependency graph, where nodes represent assumptions, operators, and claims, and edges represent inferential logic. By applying concepts from operator theory, the paper introduces metrics such as the "Rigor Deficit Functional," "Ambiguity Bandwidth," and the "Symbolic Theatricality Operator." These tools quantitatively distinguish between legitimate high-level abstraction (which maintains strict definitional closure) and performative formalism (where undefined operators cause semantic collapse). Furthermore, the manuscript examines the sociological aspects of technical communication, formalizing how institutional prestige acts as a nonlinear gain operator that amplifies the perceived validity of a claim independent of its actual proof closure. Case studies are provided, dissecting AI marketing discourse, finance terminology inflation, and machine learning overclaims. Ultimately, this work establishes a rigorous hierarchy separating productive heuristic compression from semantic drift. It provides a formal toolkit for evaluating technical integrity entirely independent of institutional affiliation, rhetorical aesthetics, or reputational priors, reinforcing the absolute maxim: notation does not replace proof, and theatrical sophistication does not replace truth.