The complete derivation of physical constants from the geometric foundation B = 1 on S². All papers are interconnected through a rigorous chain of mathematical and physical derivations.
Foundation Papers (P001–P005)
The Zero-Axiom Foundation
Establishes B = 1 on S² as the geometric foundation. The octahedral simplicial complex emerges as the unique minimal structure.
Spectral Structure of the Octahedral Simplicial Complex
Derives V=6, E=12, F=8, β₁=7 and the 48-element symmetry group O_h. Foundation for all coupling constant calculations.
The Three Coupling Constants from Octahedral Topology
Derives g₁, g₂, g₃ and sin²θ_W = 3/13 from octahedral invariants. Achieves 2.5 ppm precision on the Weinberg angle.
Fermion Masses and Mixing Angles
Derives CKM and PMNS mixing matrices from O_h representation theory. All fermion masses from geometric Yukawa couplings.
The Fine-Structure Constant from Zero Parameters
Derives α⁻¹ = 137.035999086 from pure geometry. The capacity balance equation T + c₁·α = 1 yields 12.8 ppt precision vs CODATA.
Structural Papers (P006–P008)
The Standard Model Gauge Algebra from Binary Octahedral Symmetry
Proves su(3) ⊕ su(2) ⊕ u(1) is the unique gauge algebra compatible with B = 1. Dimension 12 = E edges.
Gravity from the Null Tether Principle
Derives Einstein’s equations as the unique metric theory. Newton’s constant from octahedral invariants.
The Cosmological Constant from B = 1
Derives Λ·ℓ_P² = (9/5)·α⁵⁷ — resolves the 122 orders-of-magnitude puzzle with zero fine-tuning.
Precision Tests (P009)
Cosmology Papers (P010–P011)
Hubble Tension Resolution: H₀(local)/H₀(CMB) = 13/12
The “tension” is not an error — it’s a geometric prediction. Both measurements are correct; the ratio is N/E.
CMB Selection Rules from O_h Symmetry
Explains quadrupole/octupole suppression and alignment as O_h selection rules, not statistical flukes.
Advanced Topics (P012–P014)
Running of α from B = 1 and Perturbative Convergence
Derives the scale-dependence of α from lattice renormalization. Explains why perturbation theory works.
The Non-Perturbative Landscape of B = 1
Maps the complete solution space. Shows why the Standard Model is the unique IR fixed point.
Grand Synthesis: The Complete CMAC Derivation Chain
The complete derivation from B = 1 to all Standard Model parameters and cosmological constants. 586 identities unified.