RLMT: A Representation-Theoretic Origin for the Mode Amplitude Coefficients, and a Negative Result for Tensor-Sector Coupling

抄録

This companion paper to “RLMT: Lindblad Cosmogenesis, SU(2) Geometry, and a Numerical Confrontation with Planck 2018 Data” reports two follow-up results. First, we show that the mode amplitude coefficients C1,C2,C3, previously independent fit parameters, are fixed up to a single overall scale by identifying the N=3 tension modes with the three states of the spin‑1 irreducible representation of SU(2). This yields exact predictions C1=C2 and C3=2C1, consistent with the Planck 2018 posterior at the sub‑0.5σ level, collapsing four parameters (Beff,C1,C2,C3) to one γ=Beffk. Second, we report a negative result from an extensive search for a coupling between the Lindblad dynamics of the R‑layer and the tensor (gravitational‑wave) sector. Bilinear Clebsch–Gordan constructions give at most σ(ϵ3)/ϵ3∼0.29, while a linear population‑quadrupole postulate initially giving ∼1.06 is retracted after a microscopic Lindblad‑response check. We document two corrected implementation errors and provide full reproducibility code. We also give structural justification for RLMT’s additional parameters and discuss long‑term prospects for testing ϵ3 via future gravitational‑wave observations.