Energy-Efficient Modelology: The Thermodynamic Grammar of Model Construction, Evolution and Termination Under Finite Energy

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. Version 2. 4 introduces the MEER Audit Graph as the standard structural grammar of all models—a carrier-neutral directed acyclic graph obtained by projecting a hierarchical model onto an auditable structure under finite resource constraints. The MEER Audit Graph defines the minimal structural and dynamic requirements that any model must satisfy: nodes (model components with identifiable information contribution and estimable maintenance cost), edges (decision dependencies or shared references), a root node (presupposition), leaf nodes (testable predictions), and dynamic operations (creation, deletion, threshold adjustment, shared reference management, and metabolic audit). The MEER Audit Graph is not specific to any carrier. Its specific instances are defined in their respective domains: the Cognitive Graph in the Cognition Ontology (neural carrier), the Theory Graph in scientific methodology (institutional carrier), the Architecture Graph in AI methodology (computational carrier), and others. The MEER Tree is recovered as the special case where each non-root node has exactly one parent. The Four-Stage Protocol is the MEER Audit Graph's lifecycle: (I) Presupposition of Cause establishes the root node, (II) Formal Mapping extends the graph through modeling-level Cuts along specified Tension axes, (III) Fidelity Testing monitors the graph's health via the Response Pool A (t) and applies management strategies, and (IV) Cognitive Meltdown and Hierarchical Annealing prune dysfunctional components and graft new ones. The evolution of the MEER Audit Graph is governed by the Response Pool Equation. The Degeneration Corridor provides the thermodynamic formulation of Lakatos's degenerating research programmes. The choice between competing models is governed by the Model Energy Efficiency Ratio (MEER). The Seven Standard Modeling Techniques are composite patterns of the five primitive instructions. Cross-scale unification is achieved through Hierarchical Instantiation. The protocol achieves full self-referential closure by specifying the conditions of its own termination. Keywords: Modelology; Energy-Efficiency Theory; scientific methodology; MEER; paradigm shift; four-stage protocol; MEER audit graph; model structure graph; cognitive meltdown; hierarchical annealing; algorithmic submersion