Article 5: Gate Geometry and Accretion in Black Hole Vortices: Spiral Structure, Vacuum Core, and Vortex Dissolution in the PEW Framework

The Primordial Energy Wave (PEW) framework models all physical entities as topological vortex configurations of a single complex scalar field Ψ = ÷exp(iθ). Previous PEW articles on black holes established the Schwarzschild metric recovery, winding number hierarchy, and consistency with EHT and LIGO observations. Article 3 established that black holes carry near-zero electromagnetic charge by topological inheritance of the neutrality of absorbed matter.The present article addresses the geometric mechanism of accretion: how do ordinary matter constituents — protons, electrons, photons — enter and dissolve into the black hole vortex?We show that the black hole vortex shares the same fundamental spiral topology as the proton: a single spiral of Ψ winding into a toroidal structure with two asymmetric openings — a flared upper gate (accretion funnel, θ-sector portal) and a quasi-closed lower gate (vacuum core). The critical structural difference from the proton is the lower gate closure mechanism: whereas the proton's lower gate is constrained by the topological non-crossing condition of its three strands, the black hole lower gate closes against the vacuum of the Mother Wave itself, enforced by the λÃ⁻² term of the Lagrangian. The core is not a singularity but a vacuum bubble of radius ξ_BH ∼ 3×10⁻³⁶ m where à = Ã_min = (λ/μ²)^{1/4} = Ã_vac.Infalling vortex-particles dissolve progressively in three stages: tidal distortion, strand unwinding under external amplitude gradient, and pure phase θ absorption into the black hole spiral. Quarks de-confine not by thermal energy but by amplitude gradient compression of the proton torus below the non-crossing threshold — a continuous, geometric process with no phase transition.Relativistic jets are identified as the polar θ-escape channel opened by rotation: the only region where the waveguide condition admits outgoing modes for all frequencies, producing collimation perpendicular to the accretion disc. Information is preserved as winding number in the black hole spiral.A systematic comparison establishes that the proton and the black hole are the same object at different scales: same Lagrangian, same gate topology, same λÃ⁻² protection against singularities, distinguished only by strand number (3 vs 1), winding number (∼1 vs ∼10⁵⁷–10⁶⁶), and closure mechanism (topological vs physical).