A Primordial Vector Field: Bicomplex Charge-Space Geometry, Higgs Origin, and Unified Forces

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: P_EM (electromagnetic), P_int (elliptic, nuclear binding), and P_ext (long-range force). A single transverse function η(μ) = (Λ_QCD/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_χ^int| = |sin(πd/2A)| and nuclear binding contribution B_Φ = N·Σ₀·cos²(πd/2A) with Σ₀ ≈ 11 MeV (B_Φ/B_exp = 0.67 ± 0.06 for A ≥ 12, d > 0; B_Φ = 0 for d = 0). The external charge |q_χ^ext| is governed by conservation of scalar momentum in the Euclidean kinematic metric: p = m·|v| = constant. The velocity ratio v_xy/v_z = Λ_QCD/M_Pl ≈ 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 ∝ (m_n/M_Pl)²/r² ∼ G·m_n²/r², naturally reproducing Newtonian gravity. The Ψ interaction favors phase alignment via E_int ∝ −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).