Second-Order Regime Validity
Year: 2026
Type: article
Abstract: This paper introduces a regime-level framework for mathematical existence when admissibility is not guaranteed. It shows that bounded first-order quantities such as energy do not ensure regime persistence, and that regime validity is instead governed by second-order geometric coherence. When this coherence fails, geometry-attached time terminates and a buffer interval arises in which no regime is valid. The paper formalizes how new regimes may emerge after collapse via minimal rebirth paths selected by second-order structure, allows for multiplicity of successor regimes, and proves an exact trichotomy of observational outcomes. The framework is equation-independent and operates upstream of dynamics, clarifying when mathematical descriptions apply and how meaning can be lost and regained.
Author: Nguyen, Louis
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7119537507
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