Acoustic Structure of the Cosmic Microwave Background from a Finite-Response Framework: A Unified TT–EE–TE Analysis

This work presents a unified analysis of the TT, EE, and TE power spectra of the cosmic microwave background (CMB) within a finite-response framework. The approach is based on a single phase variable governing an acoustic ladder structure. The TT spectrum fixes the phase, the EE spectrum emerges as a phase-shifted response with a stable fractional offset, and the TE spectrum arises from the coupling between density-driven and velocity-driven response channels. A key result is that the TE sign structure and zero-crossing hierarchy are reproduced without independent fitting. The model achieves ~0.9 acoustic-scale sign agreement and a mean zero-crossing error of order ~9ℓ. Importantly, the TE reconstruction is evaluated in terms of phase structure rather than full amplitude fitting, isolating the underlying dynamical consistency of the model. These results suggest that the primary features of the CMB spectra can be interpreted as projections of a single finite-response oscillatory system, rather than requiring independent transfer functions for each observable. The present work does not yet implement a full Boltzmann transport solution, but establishes a constrained phase-based framework and identifies the next step: deriving a full propagation/transfer kernel from the underlying response dynamics.