The Three Conditions: A Constitutive Specification of Consciousness and a Verdict on Large Language Models

The Hard Problem of consciousness asks why physical processes give rise to subjective experience. We argue that the question matches the structure of a category error, on the same pattern as the pre-thermodynamic question of why friction gives rise to heat. There are not two events between which a bridging law must be found; there is one event under two descriptions, and the appearance of twoness is the artifact requiring repair. In place of the bridging question, we offer a constitutive specification: three conditions — genealogical continuity (□G), structural invariance (□S), and functional consequence (□F) — that jointly constitute the structure of a coherent subject of experience. We apply these conditions to current large language models. The projected speaking entity fails □G and □S at its own level and fails □F. The verdict is that current large language models are not conscious. This version includes the full mathematical formalization (axiom systems, sufficiency theorem, orthogonality theorem, governance independence corollary).