Abstract We derive the strong coupling constant and the complete CKM mixing hierarchy from the colour sector M3(C) ⊂ R12 of the rendering algebra, with zero free parameters. Five principal results are established. (1) ζ(Nc) Color Cohesion: the strong coupling coefficient ζ(3) is derived as ζ(Nc) = Pn −Nc , where each summand arises from Nc = 3 independent diagonal projectors of M3(C) acting on flux-tube modes weighted by the Landauer allocation wn = 1/n; alternative weightings (1/n2 , e −n , 1/n3/2 ) are excluded at > 8%. (2) Γ(Nc) = Tw: the Planck integral representation identifies Γ(Nc) = (Nc−1)! = Tw = 2 as a fourth independent condition selecting Nc = 3 uniquely. (3) CKM Cascade Upgrade: all CKM elements are promoted to A90%— |Vus| = exp[−(Nc−Z 2 )/Tw] (NLO, 2.3σ → 0.2σ), |Vcb| = |Vus| Tw × AWolf, and |Vub| = |Vus| |Vcb| × Tw C2( V2 , su(4))/N with skip factor 5/12. (4) NLO Dimension Rule: the leading Landauer correction is O(Z d ) where d is the physical dimension: Z1(EM coupling), Z 2 (CKM transition), Z 3 (colour cohesion). (5) Dual Mechanism: M3(C) produces the gauge coupling via a mode sum (αs = ζ(Nc)Z) and the CKM hierarchyvia exponential suppression (|Vij | ∝ e −C2 ). Twenty results; no free parameters.