Boundary-Induced Mode Differentiation in CMB Observables Phase-Preserving Deformation Across Projection Boundaries

This record contains the full paper: “Boundary-Induced Mode Differentiation in CMB Observables: Phase-Preserving Deformation Across Projection Boundaries” This work investigates phase deformation in the Cosmic Microwave Background (CMB) TT, EE, and TE angular power spectra from the perspective of boundary-induced effects, rather than independent primordial origins. While conventional correlation metrics suggest a rapid loss of coherence between modes at higher multipoles, this study demonstrates that the underlying phase structure is largely preserved when projection and scattering boundaries are explicitly modeled. By introducing a dispersion-adjusted phase deformation model, a common primordial identity can be recovered with high reproducibility across multipole bands. Importantly, this framework does not introduce new primordial physics, but reinterprets existing CMB observables through explicit boundary modeling, including effects from the last scattering surface, reionization history, transfer functions, and horizon-scale constraints. Supplementary Material This record is accompanied by a browser-based supplementary analysis tool implementing the exact boundary-aware phase reconstruction and identity metrics described in the paper. The tool is a paper-specific extension of an earlier prototype released at: Zenodo (previous version): https://doi.org/10.5281/zenodo.18155184 The present HTML tool is modified and extended specifically for this paper and should be cited together with the manuscript. Reproducibility No proprietary software is required All analysis runs locally in a standard web browser The supplementary tool provides direct verification of all reported results Author: Yuuki Theory ORCID: https://orcid.org/0009-0003-5736-5297