The Chinukwe Priciple/Formalism

Ergodic Sovereignty and Path-Dependent ResilienceA Mathematically Rigorous Foundational TreatiseNOTICE ON ORIGINALITY AND SCOPEThis treatise synthesizes and extends work in ergodicity economics (Peters, 2019; Peters & Adamou, 2018), classical ruin theory (Cramér, 1930; Lundberg, 1903), multi-capital theory (Becker, 1964; Grossman, 1972), stochastic optimal control (Fleming & Soner, 2006), and network contagion (Gai & Kapadia, 2010; Acemoglu et al., 2015). Peters' non-ergodic framework is the primary intellectual ancestor; the connection is explicit throughout.Novel contributions claimed are specific and narrow: (i) the multi-domain barrier distance aggregation Dᶜ with derived domain weights; (ii) the Chinukwe Coupling Matrix K with a complete spectral cascade threshold theorem; (iii) the ε-absorbing state formalism replacing binary domain partition; (iv) the residual-value boundary condition replacing the indicator-function collapse; (v) derivation of optimal regime thresholds from the HJB first-order condition; and (vi) the Falsifiability Manifesto of four sharp, rejectable predictions. All other results are labeled by type (A = restatement, B = extension, C = novel).This edition resolves 19 mathematical, conceptual, and structural gaps identified in the prior revision. Remaining open problems are explicitly flagged.