Consciousness as CRIS-Compliant Recursive Self-Modeling Under Thermodynamic Constraint

This paper presents an explicit closed falsifiable equivalence criterion for consciousness in physical systems. A system is conscious if and only if it implements a causally efficacious recursive self-model whose update dynamics are stably contractive and whose maintenance is thermodynamically solvent under continuous environmental perturbation. The criterion is formulated as four jointly sufficient and individually necessary conditions. First, nontrivial recursive self-reference via an internal self-model state that genuinely participates in its own update dynamics and carries predictive content about the system’s future. Second, identity maintenance via contraction with log-average contraction constant strictly less than one, proven to guarantee exponential decay of perturbations and robust re-identification of the self-model trajectory. Third, thermodynamic solvency via a windowed work inequality preventing both collapse and divergence, proven necessary because maintaining coherent recursive self-modeling under perturbation requires nonzero physical work proportional to uncertainty correction. Fourth, causal efficacy demonstrated by interventional changes in behavior under manipulation of the self-model state, blocking epiphenomenal constructions. The paper proves the full equivalence theorem with explicit necessity and sufficiency directions. It defines each quantity precisely, provides regime theorems connecting contraction stability to identity persistence, derives the thermodynamic work lower bound from information reduction under perturbation, and formalizes causal efficacy via structural causal models and do-interventions. Explicit preregisterable estimators and falsification targets are provided spanning anesthesia, sleep stages, dissociation, psychosis, and machine agents. First-person phenomenology is identified as the internal signature of maintaining coherent recursive self-modeling in real time at a measurable energetic cost. This paper is an official lineage derivation beneath the CRIS bedrock framework, with each of the four consciousness conditions mapping directly onto the four CRIS structural teeth.