A zero-parameter derivation of fundamental physics
0 Axioms
0 Free Parameters
586 Identities
67 Predictions
What is CMAC?
The Constraint-first Mathematical Architecture of the Cosmos (CMAC) is a research programme that derives the structure of fundamental physics from a single geometric constraint:
$$B = 1 \text{ on } S^2$$
From this constraint alone — with zero axioms and zero free parameters — the programme derives the Standard Model gauge algebra, coupling constants, and particle masses.
The Arena
The unique arena satisfying $B=1$ is:
$$\mathbb{CP}^1 = S^2 = SU(2)/U(1)$$
This is the complex projective line — equivalently, the 2-sphere or the coset space of SU(2) by U(1).
Emergent Structure
The octahedral group $O_h$ emerges as the maximal discrete symmetry, with invariants:
These are not inputs — they are derived from the single constraint $B=1$.
Key Results
| Observable | CMAC Value | Precision | Tier |
|---|---|---|---|
| $\alpha^{-1}$ | α⁻¹ = 137.035999086 | 12.8 ppt | PHYS-DERIVED |
| $\sin^2\theta_W$ | sin²θ_W = 3/13 | 2.5 ppm | PHYS-DERIVED |
| Hubble ratio | H₀(local)/H₀(CMB) = 13/12 | 0.02σ | PHYS-DERIVED |
Epistemic Tiers
All 586 identities are rigorously classified:
| Tier | Definition | Count |
|---|---|---|
| MATH-PROVEN | Machine-verified mathematical proof | 258 |
| PHYS-DERIVED | B=1 plus one physical identification step | 67 |
| STRUCTURAL | Pattern match requiring future proof | 261 |
| CONJECTURAL | Gaps remain in derivation | 0 |