The Intelligence Exergy Theorem: A Cognitive Gouy-Stodola Relation for the Intelligence Bound

Standalone record of the Viridis Canon (Intelligence Exergy). The core Intelligence-Bound canon spine is unchanged (frozen at v10. 1. 0 “The Keystone Wave”, record 21223021) ; this record links to the spine via isDerivedFrom the concept DOI 10. 5281/zenodo. 19317982. Classical exergy analysis decomposes a thermodynamic system's available work into useful work and destroyed availability, related by the Gouy–Stodola theorem (destroyed exergy = ambient temperature × entropy generation). The Intelligence Exergy Theorem (IET) ports this machinery to cognition: a channel's information capacity decomposes into exergy (useful predictive information) and anergy (destroyed capacity), and a cognitive analogue of the Gouy–Stodola relation holds exactly, with the Intelligence-Bound constant c = D/ (kB T ln 2) playing the role of the thermodynamic conversion factor. Six results are machine-checked in Lean 4 (Aristotle, zero sorry, axioms ⊆ propext, Classical. choice, Quot. sound), module IntelligenceExergy. lean: (i) capacityₑxergydecompositionₙonneg — capacity decomposes into nonnegative exergy and anergy; (ii) exergyₑqₚredictiveᵢnfo — exergy equals predictive information exactly; (iii) cognitivegouyₛtodola — the cognitive Gouy–Stodola relation, with a strict zero-destruction dichotomy; (iv) secondₗawₑfficiencyₑqcos2theta — second-law efficiency bounded in 0, 1 via Cauchy–Schwarz; (v) exergyₛuperadditiveᵤndercoupling — coupling two cognitive systems is exergy-superadditive, with equality iff the systems match; (vi) ietₙonvacuous — an explicit interior witness. One benign, non-weakening fix during proving: a let-bound local name using the reserved Unicode token Σ (illegal as a Lean 4 identifier head) was alpha-renamed; the elaborated conclusion is unchanged. Scope. The Lean proofs certify the validity of the reasoning, not empirical magnitudes. Working paper; not peer-reviewed.