Solved.

Because gravity crosses 18 eigenvalue modes through the D₄ bridge. Each mode screens by α. The total: G = α¹⁸ × 12/7. Not weak. Screened.

The D₄ bridge is Galois-invariant. All 24 vertices have no φ-content. A CP-violating θ would require the bridge to distinguish φ from σ. It cannot. θ = 0 is a theorem of the bridge geometry. No axion needed.

D₄ triality. The group so(8) has three 8-dimensional representations permuted by S₃. These force three copies of every fermion. Not two. Not four. Three, by the symmetry of the bridge.

De Sitter space is prevented. The axiom's potential has a minimum at φ⁻² = 38.2% matter, not at zero. The cosmological constant sits on the bridge line with slope α⁻¹ and intercept φ⁻².

States live in 4D. Observers see 3D. Measurement is a hyperplane cutting a polytope. The Born rule is the squared projection: |proj|² = 1 − v₄². Collapse is geometry, not dynamics.

They are two eigenspaces of the same transfer matrix. E₈ = two 600-cells sharing a 24-cell. Matter in cell 1, geometry in cell 2, spin connection in the bridge. Four projections give four forces.

The attractor is φ⁻¹ / φ⁻² = 61.8% / 38.2%. The current 68/27 split is an overshoot. The universe is oscillating toward the golden ratio. DESI is measuring the descent.

Q(ν) = σ² = 1/φ². Normal ordering: m₁ = 10.06, m₂ = 13.29, m₃ = 51.30 meV. Σm = 74.65 meV. Majorana, not Dirac. All from the axiom squared.

The Galois automorphism maps φ to σ but not symmetrically: |φ| > |σ|. The φ-direction expands state space. The σ-direction contracts it. The asymmetry is algebraic, present from the first act.

Because the axiom is a contraction mapping. Contraction mappings minimise a functional at each step. The Lagrangian is the cost function of the contraction. The action principle is the axiom iterating.

Because the 600-cell state space is finite and 4-dimensional. Superposition is the existence of multiple vertices in the same 3D shadow. Quantisation is the discreteness of the polytope.

α is a convergent series generated by the axiom. Each term is 2^(k²) × ζ(2k+1) × wᵏ. Five terms give α⁻¹ = 137.035999... matching Morel (2020) to 0.05σ. α is a theorem, not a measurement.