This paper establishes two results within the Quantum Gauge Theory of Time (QGT). First result: the spectral factor as loop gain. The correction factor f = (2√5) ^ (3/2) / (3π) ≈ 1. 003463 is the holonomy-normalised loop gain of the global Phase-Locked Loop (PLL) formed by the boundary breathing equations. The complete spectral factor Fₙm = (2√5) ^ (5/2) φ²/ (9π²) closes the dimensional cascade R∞ → f_τ → R₅ → G → ℓP → TCMB with R∞ as the unique external metrological anchor. Physical time is the output of this PLL. Second result: TCMB without R∞. At the decoherent floor n=0, where all admissible modes are extinct, the Majorana 5D condition (Δφbulk = 4π), the Cayley conformal map (θ=π is the fixed point of physical time), and the entropic prime number theorem (PNT-E, Φₖ → π) together force Γ_τ^ (0) = 4π. The entropy per decoherent oscillation is ln π. The intrinsic floor temperature is TCMB = (π/ln π) (1 − 1/ (√2·100) ) = 2. 724991 K residual 0. 86σ from Fixsen et al. (2009). R∞ is not required. The Kelvin scale is not an external input: it emerges from π, the fixed point of the Cayley map and the arithmetic attractor of the Majorana 4π cycle. The two derivations are independent: the first gives TCMB given R∞; the second gives TCMB from the structure of the decoherent boundary alone.
Pasquale Camelia (Wed,) studied this question.