Paper 72: A Proof-of-Concept Shell-Resonance Solver for Low-ℓ CMB Structure in Holosphere Theory

This paper develops a proof-of-concept computational model for large-scale structure in the Cosmic Microwave Background (CMB) within Holosphere Theory. The model treats the CMB not purely as a frozen relic of early-universe acoustic oscillations, but as a resonance pattern supported on a rotating coherence shell in a discrete lattice of angular phase elements. The analytic scaffold of the model proposes a base resonance ladder in multipole space, calibrated using the first major CMB peak near ℓ≈220. In this framework, the fundamental spacing scale is expressed as ℓₙ = π ε n with ε ≈ 70. A second conceptual layer introduces triadic interference, motivated by three-way phase-closure interactions in the Holosphere lattice, which can shift observed peaks away from the base integer ladder. The central contribution of this work is computational rather than purely analytic. An axisymmetric proof-of-concept shell solver is implemented that evolves a real-valued angular phase field over polar angle and projects the late-time field onto Legendre multipoles. Parameter sweeps reveal a stable resonance basin that produces reproducible low-ℓ spectral structure in the correct broad multipole regime. The current solver does not yet reproduce the full Planck TT spectrum. The best runs still require amplitude rescaling and a non-zero multipole shift when compared to a target spectrum, and the admissibility gating mechanism is not yet strongly structuring the winning basin. However, the results demonstrate that shell-supported Holosphere dynamics can generate stable resonance patterns computationally rather than only at the level of analytic suggestion. Paper 72 therefore serves as a feasibility and falsifiability paper. It establishes the shell-resonance scaffold, demonstrates the first working solver, identifies a reproducible parameter basin, and defines the next steps required for a full spherical CMB solver and a more complete interference derivation.