The Mathematical Core: Formal Foundations of the Five Principles v2.3

Formal definitions, propositions and theorems for the Five Principles framework, written as a candidate model of how organised systems emerge, evolve and integrate through relationships and constraints. The document defines coherent and decoherent cores and a transition zone, treats the label process as a metastable approximation, gives an Eyring–Kramers transition-rate result with its stated hypotheses and scope, and lists falsifiable predictions with their conditions. It is a candidate model, not a universal law, and it makes no claim about cosmological origin. Prior art is cited to primary sources, including Landauer, Kramers, and Bovier, Eckhoff, Gayrard and Klein (2004). Known limitations are listed in the document, including that the multidimensional escape-rate theorem as printed in its source does not cover every well-to-well direction used here, that one numerical experiment has no script attached, and that one invariance criterion has no source stating it exactly. The text was revised with AI review (DeepSeek, Kimi, ChatGPT, Gemini, Claude). These are method checks, author-reported, and not independent peer review.