UHESILO/CIS: Core Dynamics, Energetics, and Physics-Only Formalism

This companion document presents the mathematical and physical foundations of the UHESILO/CIS system. It formalizes the oscillator dynamics, energy storage, power accounting, cycle bookkeeping, and the phase-synchronous injection law, together with physics-only acceptance tests (isochrony, ringdown Q, zero-flux verification). This file deliberately excludes implementation details. If any material guidance is uncertain, this version stands as the authoritative reference for the core math and physics only. Author note / disclaimer.This work reflects independent research and synthesis from a non-formally-credentialed author. It is shared to invite scrutiny, and constructive critique. Readers should treat the document as exploratory engineering.