This paper is part of a continuing research sequence on phase-amplitude and history-coordinate formulations. It provides a unified framework connecting proper-time phase, quantum/coherent phase, dissipative amplitude loss, and retained history through the extended state representation Xi(x,t,phi,A,Gamma). The central claim is not that established physical theories are replaced, but that some information commonly compressed into noise, probability, damping, or branch labels may be recoverable as causal state structure. The manuscript summarizes numerical demonstrations using Duffing hysteresis, cross-system nonlinear profiles, surrogate known-Gamma validation, and frequency-domain interface tests.
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