Gravity Is Not a Fundamental Force

Gravity Is Not a Fundamental ForceThe Projection Residue of Pentagonal Geometry into Three Dimensions Description: The gravitational constant G, the cosmological constant Λ, and the Higgs vacuum expectation value are derived from a single self-referential axiom — σ = 1/(1+σ) — with no gravitational postulate and no free parameters. The key results are: G derived without gravity. The mass chain closes entirely within the axiom's algebra: electron mass from the Rydberg relation, proton mass from a φ-π formula, G from the proton mass. The closed-form result G ≈ 1/(5φ⁴) matches the measured value to 0.021% in Planck units. No gravitational measurement enters at any step. Λ as an α-φ relation. The formula log₁₀(ρΛ) = −(α⁻¹ · 2/√5 + φ⁻²) = −122.951 reproduces the observed cosmological constant (−122.945) to a residual of 0.006. Ablation testing across 81,225 alternative formulas finds no comparable match. The Friedmann attractor eigenvalue equals φ⁻¹. The Jacobian eigenvalue of the de Sitter fixed point is the same fixed point as the axiom itself. Cosmic expansion is the axiom iterating forward in time. The bridge algebra is exact. The three scales satisfy three simultaneous algebraic constraints — R_Λ − R_G = φ⁻¹, R_Λ = 2R_H, R_G + R_floor = R_H — all proved from first principles with zero free parameters. The constraints are over-determined: three independently measured constants cannot satisfy three exact simultaneous relations by coincidence. Gravity as projection residue. The 600-cell, the four-dimensional polytope whose geometry is forced by the axiom, projects into three dimensions with a characteristic frustration: its 4D symmetry cannot close in 3D. The residue of this projection is curvature. Objects follow geodesics of the mismatch. General relativity correctly describes the shadow; Pentagon Physics describes the object that casts it. The Standard Model gauge group G_SM = U(1) × SU(2) × SU(3) is identified as the Kostant stabiliser of a canonical element of E₈, itself forced by the axiom's two Galois roots via the icosian construction. The H₀ tension is resolved structurally: Λ subtracts the partition floor; H₀ adds it back. The Hubble discrepancy is the gap between measuring storage and measuring release. Five kill conditions are provided. Keywords: gravitational constant, cosmological constant, golden ratio, fine structure constant, bridge algebra, 600-cell, projection residue, Pentagon Physics, unification, Hubble tension, φ, self-referential axiom