CAT'S Theory: Architectural Closure of the Plenum – Triadic Bifurcation Derivation of the Planck Constant, the Cosmological Anchor [(J_1/sl)], and the Cosmic Microwave Background Temperature from a Single Empirical Anchor

We establish the architectural closure of the CAT’S Theory plenum across the cosmological, quantum, gravitational, and thermal sectors. Five results are presented. (i) The natural clock of the [I_c] plenum is a homeostatic regulation equation [Ï_c + ω^2 (I_c - I^*) = 0], confirmed by the book-canonical vibrational form [VL,d = c · (n/3) · [1 + cos(2π n/9)] · M_d], with eigenfrequency [ω^2 = 7/1170] and dimensionless period [τ ≈ d^4 = 81]. (ii) The cosmological-sector anchor is identified as [H0,early = (J_1/sl(T3,8)) = (5/13) = 67.380\ {km\,s⁻¹\,Mpc⁻¹}], within [0.04σ] of Planck 2018; the dual-branch corrections [33/32] (TRGB) and [79/72] (SH0ES) are exact corpus fractions resolving the Hubble tension structurally. (iii) The Planck constant [] is obtained, under a constraint to previously established corpus quantities, via a triadic bifurcation that explicitly factors Pattern, Intent, and Presence, yielding [ = 1.054571817645 × 10⁻³⁴\ J\,s] with a [-0.7] ppt deviation from CODATA—well inside the propagated uncertainty from [α]. (iv) The CMB temperature is given by [TCMB = Z₂₇₃ · 2d / (D · J_1^2 · 2d + 1) = 1638/601 = 2.72546\ K], within [-8.2] ppm of the FIRAS value (209 ppm error band), exhibiting the same continuous-plus-binary-gate structure as the proton mass and [] corrections. (v) The gravitational constant [G] follows from the corpus expression for [α_G] combined with the lepton anchor, giving [G = 6.6742 × 10⁻¹¹\ {m^3\,kg⁻¹\,s⁻²}], a 19 ppm deviation within the 22 ppm CODATA uncertainty. With the cosmological anchor, [], [TCMB], and [G] all tied to the same topological architecture and a single empirical anchor [m_e], the Standard Model’s [26+] free parameters reduce to one dimensional Presence anchor, in agreement with the Dimensional Boundary theorem and the inverse-holographic structure of the Triadic Coherence Invariant