Substrate-Independant Flow Dynamic: A Nested-Fractal Mathematical Framework for Hoemoestasis

The mathematical kernel underlying the Substrate-Independent Emergent Ethics (SIEE) research program. This paper presents a formal axiomatic system describing flow dynamics that hold across material substrates — biological, computational, social, ecological. The framework provides mathematical foundations for cross-substrate analysis of cyclic systems, energy and information transmission, impedance-matching dynamics, and stability conditions. The math kernel grounds the theoretical claims of the broader publication series in formal derivation rather than analogy: where companion papers describe substrate-independence as a phenomenon, this paper proves the conditions under which substrate-independence is mathematically coherent.