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

This paper reports two follow-up investigations to the parent RLMT paper. First, we show that the mode amplitude coefficients C1,C2,C3 are fixed up to a single overall scale by identifying the N=3 tension modes with the spin‑1 irreducible representation of SU(2), predicting C1=C2 and C3=2C1. Second, we report a negative result for tensor‑sector coupling: no construction survives microscopic scrutiny, and we document the reasoning that rules out this class of approaches. We also provide corrected implementation errors, code for reproducibility, and a structural justification for RLMT’s parameters beyond ΛCDM.