Part 26: Quantitative Signatures of Antimatter Leakage in Dual–H4 Geometry: A Parameterized WKB Source Model for Positron-Dominated Cosmic-Ray Observables

Overview Within the framework of Origin Geometry (OG), the dual-sector architecture H₄ ∪ φH₄ allows the visible (H₄) sector and the phase-shifted (φH₄) sector to coexist within a shared geometric substrate while remaining strongly misaligned at the level of boundary-supported modes. Previous Parts developed the interpretation of dark matter as hidden geometric stress, topological pinning, near-flat-band freezing, reduced electromagnetic accessibility, dark-sector compression, and effective dark collapse [1–5]. Part 25 introduced a qualitative mechanism by which antimatter-like excitations sequestered in the (φH₄) sector may leak weakly into the visible sector through extreme curvature regions. The present Part develops a parameterized order-of-magnitude framework for that mechanism. Its goal is not to fit cosmic-ray data, derive a complete transport theory, or calculate absolute fluxes from first principles. Instead, it identifies the mathematical parameter combinations that control whether rare inter-sector leakage could generate observable positron-biased signatures. WKB-Like Tunneling and Mass-Asymmetric Filtering The central ingredient is WKB-like tunneling through an effective topological phase barrier [6]. For an excitation species i, the leakage probability is modeled as: P_i ~ exp[−S_i] where: S_i = (2/ħ) ∫ [from x₁ to x₂] √(2m_i,eff [V_phase(x) − E_i]) dx In a uniform-barrier approximation: S_i ≈ (2 L_eff / ħ) √(2m_i,eff V_eff) The WKB action scales as √(m_i,eff). Therefore, if the dark-sector effective mass hierarchy satisfies [7]: m_p̄,eff ≫ m_e+,eff then positron-like modes tunnel far more efficiently than antiproton-like modes under comparable barrier conditions. This produces mass-asymmetric filtering [8, 9]. Unlike the earlier qualitative version, the present Part does not assume that a larger dark-sector boundary mass inflation automatically preserves positron dominance. Instead, it writes the effective masses as: m_p̄,eff = χ_p̄ m_p m_e+,eff = χ_e m_e and states explicitly that positron-dominated leakage requires: χ_p̄ m_p ≫ χ_e m_e This condition is central. If it fails, WKB filtering no longer favors positron-like leakage. Parameterized Source Term The leakage source term is also written in dimensionally consistent form. A microscopic tunneling probability P_i is not itself a rate. A leakage rate per source requires an effective attempt frequency ν_att: Γ_i,src ~ ν_att P_i A corresponding source density may then be parameterized as: Q_i(r,E) ~ n_src(r) N_i,hid(r) ν_att(r) P_i(r) f_i(E) or equivalently in terms of a dark-sector density reservoir: Q_i(r,E) ~ η_i [ρ_dark(r) / m_i,eff] Γ_i(r) f_i(E) Here n_src is the density of barrier-weakening environments, N_i,hid is the number of hidden excitations available per source, η_i is an effective leakage efficiency, and f_i(E) is an injection spectrum.