1 Introduction This paper closes every question it opens. Papers I and II established a chain from SU(2) vertexgeometry to a parameter-free spectral prediction. The present paper confronts that predictionwith Planck data, executes the independent LQC Bogoliubov calculation that was left open,and resolves the status of the conformal scale ηB.The answer to the Bogoliubov calculation is unambiguous: the LQC bounce generatesPlanck-scale mode mixing at τH ≈ 4 × 10−31Mpc/c, separated from the CMB window by34 orders of magnitude in comoving scale, with no mechanism to bridge the gap. The matchingcondition ηB = √2η0/ℓ0 does not emerge from LQC dynamics — it is a geometric condition onwhen the SU(2) zero aligns with a chosen CMB multipole. Within this framework, ηB is a freeobservable parameter.The framework is now complete: firm predictions clearly distinguished from constrainedparameters, and no open questions remaining within the scope of this series.
Hillard et al. (Thu,) studied this question.