Paper 73: Harmonic Modulation Constraints for the CMB Shell–Resonance Program in Holosphere Theory

This paper develops a constrained harmonic-envelope hypothesis for the Holosphere CMB shell-resonance program. Building on Papers 71 and 72, it does not attempt a full cosmological fit or a complete first-principles derivation of the Cosmic Microwave Background spectrum. Instead, it asks a narrower question: what kinds of harmonic modulation envelope are mathematically compatible with the shell-resonance scaffold already proposed, and what observational tests could falsify them? The paper begins from the shell-resonance ladder inherited from the earlier CMB papers and combines it with a triadic phase structure motivated by Holosphere coherence geometry. From these ingredients it identifies a general multi-harmonic envelope family and then studies a minimal working version in which the phase offsets follow a linear law. This leads to a sharp observational consequence: trough locations should organize into shifted harmonic families tied to the shell scale and, under the linear phase law, should share a common horizontal offset in multipole space. The paper also distinguishes between short-persistence and extended-persistence regimes, depending on how rapidly higher harmonics weaken. To clarify the computational status of the proposal, the paper uses synthetic benchmark spectra rather than real observational fits. These benchmarks show that the analysis pipeline can distinguish among baseline, first-order, and multi-harmonic injected targets without artificially favoring the most complicated model. This result supports internal consistency and demonstrates that the benchmark machinery behaves fairly, but it does not establish observational confirmation. The central contribution of Paper 73 is therefore methodological as much as physical. It turns the Holosphere CMB program into a more sharply defined modulation hypothesis with explicit falsifiers. If later observational work supports the envelope structure, the CMB could be interpreted not only as a peak sequence but as the signature of large-scale angular coherence shaped by resonance, interference, and finite coherence cutoff. In the present paper, however, that broader interpretation remains provisional.