LM The Impossibility Suite

This paper consolidates a set of core impossibility results governing admissible inquiry, explanation, and legitimacy. It establishes that certain operations commonly assumed to be available in foundational reasoning are not merely difficult or unimplemented, but structurally impossible under admissibility and standing preservation. The suite demonstrates three central impossibilities:(1) legitimacy cannot be generated,(2) legitimacy cannot be transferred across domains or by association, and(3) legitimacy cannot be repaired once lost. These results are not empirical claims and do not depend on technological limits. They follow from exhaustion-based analysis of admissible reasoning and apply uniformly across physics, mathematics, artificial intelligence, and epistemic governance. The paper functions as a boundary theorem: it prevents illicit appeals to explanation, success, consensus, authority, or post-hoc justification as sources of legitimacy. Any framework that violates these impossibilities collapses standing, regardless of performance or coherence. No constructions, enforcement mechanisms, or operational procedures are provided. The results are declarative, binary, and auditable in principle. Keywords: impossibility results, admissibility, standing, legitimacy, epistemic limits, foundational constraints