Limiting Cases as Regime Architecture in Physics

Abstract

Limiting cases are commonly treated either as mathematical operations on equations or as formal relations between successive theories. Neither treatment explains what makes a limit physically significant, how several operations cooperate in actual cases, or why limiting relations matter even when they do not establish reduction. This article develops a regime-architectural account. A limiting-case relation is physically licensed when an admissible class of parameter paths, a domain of application, mappings between relevant structures, mediating operations, an independently fixed recovery criterion, and two evidential stages form a connected constraint system. Its structure is represented as : establishes that physical systems occupy the stated regime, whereas independently tests the regime predictions generated by the preceding components. This separation blocks circular licensing. Universal constraints of path admissibility, prospective error control, evidential independence, and robustness give the framework exclusionary and normative force while leaving the physical content of each component case-specific. Effective field theory supplies a technically mature instantiation; categorical formalisms illuminate mappings and equivalence but do not replace physical parameter paths, domains, or evidence. Newton’s polygonal construction in Proposition I of the Principia provides a historical prototype. The Newtonian regimes of relativity and the quantum-classical transition exhibit regular and compound recovery, while phase transitions establish singular regime organization. Limiting cases thereby produce depth unification and epistemic compression: they specify which effective descriptions apply, how their domains are connected, and what would falsify the connection. This is a preprint version of a manuscript currently under journal review.