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 Highly Recommended reading order to understand the framework as its not practical to reproduce the primitive stack in every downstream paper: Foundational Closure of Admissibility and Standing: Non-Derivability, Minimality, and the Kernel of Non-Degenerate Reasoning — establishes the non-derivable kernel and the transcendental argument structure inherited by the later papers. Foundational Closure of Admissibility and Standing Necessity of Admissibility in Non-Degenerate Compositional Systems: AMetric Boundary, Bivalence, and the Unique Admissible Interior — technical core; derives the forced interface shape from the minimal compositional base. Necessity of Admissibility in Non-Degenerate Compositional Systems The Mathematics of Coherent Reasoning: A Bivalent Trajectory Theory — derives the finite path geometry over the fixed substrate and is the most downstream/mathematically transparent presentation of the internal consequence layer. The Mathematics of Coherent Reasoning: A Bivalent Trajectory Theory