ζ(Nc) Color Cohesion, CKM Casimir Cascade, and the Complete M3(C) Sector of the R12 Rendering Algebra
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 hierarchy
via exponential suppression (|Vij | ∝ e −C2 ). Twenty results; no free parameters.
Related
- The 12-gon Area Identity, Defect Operator, Stabiliser–Casimir Duality, and the Derivation of α−1 from the R12 Rendering Algebra
- The Barbero–Immirzi Parameter, Black-Hole Entropy, and the Area Gap from the R12 Rendering Algebra: McKayFolding, the SU(2)4 Horizon Category, and the Complete Entropy Expansion
- Spacetime Existence, Structure, and Expansion Rate from the R12 Rendering Algebra: A Complete Top-Down Derivation with Zero External Physics
- Single-Field Inflation from the Rendering Algebra: Complete Derivation via Icosahedral Geometry
- The Hubble Ladder: Complete Self-Referential Classification of H0 Measurements and the φ-Rung Spectrum of the R12 Rendering Algebra
BibTeX
@misc{lim2026ζnc,
title = {{ζ(Nc) Color Cohesion, CKM Casimir Cascade, and the Complete M3(C) Sector of the R12 Rendering Algebra}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23625091},
url = {https://zenodo.org/records/23625091},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - ζ(Nc) Color Cohesion, CKM Casimir Cascade, and the Complete M3(C) Sector of the R12 Rendering Algebra
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23625091
UR - https://zenodo.org/records/23625091
AB - 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 hierarchy via exponential suppression (|Vij | ∝ e −C2 ). Twenty results; no free parameters.
ER -