We postulate a primordial vector field in a four-dimensional internal charge space equipped with the algebra of bicomplex numbers. The state metric is Minkowskian with signature (+, +, +, -) and symmetry group SO (3, 1) ; a separate Euclidean kinematic metric governs particle motion. The field is a massive Proca field with bare mass M₀ ∼ H₀ ∼ 10⁻³³ eV in all four directions; the electromagnetic U (1) emerges as an accidental global symmetry of the low-energy effective theory, evading the Weinberg-Witten theorem. Two exact algebraic dualities structure the particle content: S₁ (electron ↔ proton) and S₂ (photon ↔ neutron). The Higgs mechanism deforms the state metric, generating masses while preserving the dualities. The neutron becomes a null vector — a geometric origin for β-decay — while the photon remains space-like. The Higgs generates m_Φ ∼ 140 MeV for the neutral charge field Φ, and the long-range field Ψ obtains its mass from spacetime curvature: m_Ψ ∼ H₀. The charge space contains three planes: PEM (electromagnetic), Pᵢnt (elliptic, nuclear binding), and Pₑxt (long-range force). A single transverse function η (μ) = (ΛQCD/μ) ² controls all dimensionless hierarchies; η (v) matches the Higgs coupling λ_χ to within 2%. Quarks are decomposition basis vectors constrained by charge-space quantization, giving geometric confinement. Nucleons are oscillatory signals; protons are Φ-inert by S₁, while neutrons drive nuclear binding by S₂. The collective elliptic rotation of all N neutrons yields internal neutral charge |q_χⁱnt| = |sin (πd/2A) | and nuclear binding contribution B_Φ = N·Σ₀·cos² (πd/2A) with Σ₀ ≈ 11 MeV (B_Φ/Bₑxp = 0. 67 ± 0. 06 for A ≥ 12, d > 0; B_Φ = 0 for d = 0). The external charge |q_χᵉxt| is governed by conservation of scalar momentum in the Euclidean kinematic metric: p = m·|v| = constant. The velocity ratio vₓy/vᵦ = ΛQCD/MPl ≈ 10⁻¹⁹ is a boundary condition fixed at the electroweak transition, setting the projection factor for Ψ. The coupling is g_Ψ ∼ O (1), with the force F_Ψ ∝ (mₙ/MPl) ²/r² ∼ G·mₙ²/r², naturally reproducing Newtonian gravity. The Ψ interaction favors phase alignment via Eᵢnt ∝ −cos (δ₁−δ₂) ; coherent HI disks enable macroscopic forces while lattice-locked phases in solids suppress them by ∼10¹². The model reproduces the Bethe-Weizsäcker symmetry term, explains flat galactic rotation curves without dark matter, and unifies the dark sector through m_Ψ ∼ H (t).
Ricardo Morales Velásquez (Tue,) studied this question.