Energy Conservation as a Degenerate Case of Structural Integrity: A Structuristics Derivation

Richard Feynman observed that physics has no knowledge of what energy is, since every available definition is circular: energy is defined as the capacity to do work, and work is defined as the transfer of energy. Noether's theorem connects energy conservation to time-translation symmetry but does not explain why the symmetry holds or what governs its local violation. This paper argues that both gaps share a common root: the language required to address them was absent. The language is provided by Structuristics (Moura, 2026), a formal framework that defines Decompositional Integrity as the normalised measure of how much of a system's structure survives a decomposition-reconstruction cycle under a specified decomposition operator. Instantiating Structuristics in the physical domain, where Decompositional Integrity equals the quantum survival probability, and connecting the framework to the Mandelstam-Tamm inequality, this paper derives four results. First (H1, Inference): energy conservation is the degenerate case of the Homeostatic regime, holding because and only while the decomposition operator does not act on the system. Second (H2, Inference with one Hypothesis prediction): quantum violations of energy conservation are Corrigible-regime excursions at minimum duration, bounded by the Mandelstam-Tamm time. Third (H3, Inference): energy is a relational property of the system-decomposer pair, which dissolves the circularity Feynman identified by showing that demanding an intrinsic definition is a category error. Fourth (H4, open problem): mass-energy equivalence is identified as a candidate for interpretation as a total Reconstitutable transition, with explicit closure conditions stated. A non-circular definition of energy is proposed, grounded in the rate of change of Decompositional Integrity, making no reference to work, capacity, or force. Five figures are included: a historical context timeline, a structural integrity dial illustrating the three-regime framework, a visualisation of the Mandelstam-Tamm inequality, a diagram contrasting the circular standard definition with the non-circular structural definition, and a visualisation of the structural hierarchy of isolated quantum systems. The document is produced under CAMAF CS2 standards (Moura, 2026), with full epistemic labelling, two falsifiable predictions, a Non-Assertion Declaration, and explicit limitations.