Energy-Efficient Modelology: The Thermodynamic Grammar of Scientific Evolution

What is the optimal method for constructing and evolving models under finite energy? Popper offered falsificationism, Kuhn described paradigm shifts, and Lakatos proposed the methodology of scientific research programmes. Yet none grounded their prescriptions in the physical constraints of cognition itself. Energy-Efficiency Theory (EET) provides the missing thermodynamic foundation. This paper establishes Energy-Efficient Modelology as the constitutional methodology of EET. We derive the irreducible Three-Step Modeling Protocol—presupposition of cause, formal mapping, and fidelity testing—from the dual constraints of Finite Actionability and the unattainability of Absolute Truth. This protocol is not a heuristic choice but a thermodynamic necessity: any finite agent must truncate infinite causal regress, compress natural causality into rule causality, and validate models against real-space energy exchange. The evolution of models is governed by the Response Pool Equation inherited from Constraint Dynamics. Anomalies accumulate as A (t) ; when A (t) Eb^melt, the model undergoes Cognitive Meltdown—the thermodynamic mechanism underlying Kuhn's paradigm shifts. When is insufficient to sustain Proper Pseudo-Truth yet A (t) < Eb^melt, the model enters the Degeneration Corridor, accumulating ad hoc parameters that harden the protective belt and increase Eb^melt. This is the precise thermodynamic formulation of Lakatos's degenerating research programmes. The choice between competing models is governed by the Model Energy Efficiency Ratio (MEER): MEER = (H (P) - D₊₋) / (C (Q) ). Proper Pseudo-Truth is the model that maximizes MEER under current constraints. This provides a quantitative, first-principles resolution to the problem of theory choice that eluded both Kuhn and Lakatos. Cross-scale unification is achieved through Hierarchical Instantiation: the same modeling grammar operates from quantum mechanics to civilizational dynamics, with core parameters (, Eb, L) instantiated via level-appropriate proxies. This version restores all detailed arguments, examples, and cross-ontology interfaces that were compressed in prior outputs. It integrates explicit bridges to Energy Dualism, Inverse Entropy, the Spectrum, Xu-Shi, and the Observer. A comprehensive appendix of 14 deep insights (L3 EXTENDED) synthesizes the philosophical and mathematical implications. Keywords: Modelology; Energy-Efficiency Theory; scientific methodology; MEER; paradigm shift; Lakatos; Kuhn; Popper; theory choice; degenerating research programmes