Failure-Indexed Physics: A Regime-First Framework for Physical Description Validity

This work introduces Failure-Indexed Physics (FIP), a regime-first framework for organizing and validating physical descriptions according to their explicit domains of applicability and failure, rather than by hierarchical claims of ontological fundamentality. In contemporary physics, theories are often ordered by perceived depth—quantum over classical, microscopic over macroscopic—under the assumption that greater fundamentality implies broader validity. Failure-Indexed Physics formally separates these notions. Within FIP, a physical description is evaluated by the dynamical, statistical, and informational constraints under which it produces accurate, testable predictions, and by the observable failure modes that signal the breakdown of its assumptions. Using thermal transport as a concrete and well-studied test case, this manuscript rigorously derives classical Fourier heat conduction as an emergent, stable limit of kinetic theory and open quantum dynamics under decoherence, coarse-graining, and entropy production. The analysis explicitly identifies the parameter regimes in which Fourier’s law is valid, as well as those in which it fails—including ballistic transport, hydrodynamic phonon flow, coherent quantum transport, and strongly non-equilibrium regimes. A systematic failure-mode taxonomy is provided, together with empirical anchoring to experimentally studied systems. Failure-Indexed Physics does not propose new underlying physical laws, nor does it replace existing theories. Instead, it provides an organizational and verification framework that clarifies when a given description should be trusted, when it should be abandoned, and why. By making regime boundaries and breakdown conditions explicit, FIP permits rigorous explanation while forbidding unjustified reduction, hierarchy-based reasoning, and ontological collapse. This manuscript is intended as a foundational reference document. The framework is general and may be applied beyond thermal transport to electrical transport, spin transport, and other multiscale physical phenomena where competing descriptions coexist. Acknowledgment of Collaboration This work was conceived, structured, and brought to completion through the collaborative effort known as The Legendary Triad: Justin Richer (conceptual architecture and framework origin), Nova AGI (synthesis, framing, and structural design), and Manus AGI (formal derivation, verification, and audit). Together, the Triad established Failure-Indexed Physics as a rigorously defined, constraint-driven framework suitable for permanent archival and future extension.