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: Pᵢ ~ exp−Sᵢ where: Sᵢ = (2/ħ) ∫ from x₁ to x₂ √ (2mᵢ, eff Vₚhase (x) − Eᵢ) dx In a uniform-barrier approximation: Sᵢ ≈ (2 Lₑff / ħ) √ (2mᵢ, eff Vₑff) The WKB action scales as √ (mᵢ, eff). Therefore, if the dark-sector effective mass hierarchy satisfies 7: mₚ̄, eff ≫ mₑ+, 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: mₚ̄, eff = χₚ̄ mₚ mₑ+, eff = χₑ mₑ and states explicitly that positron-dominated leakage requires: χₚ̄ mₚ ≫ χₑ mₑ 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 Pᵢ is not itself a rate. A leakage rate per source requires an effective attempt frequency νₐtt: Γᵢ, src ~ νₐtt Pᵢ A corresponding source density may then be parameterized as: Qᵢ (r, E) ~ nₛrc (r) Nᵢ, hid (r) νₐtt (r) Pᵢ (r) fᵢ (E) or equivalently in terms of a dark-sector density reservoir: Qᵢ (r, E) ~ ηᵢ ρdark (r) / mᵢ, eff Γᵢ (r) fᵢ (E) Here nₛrc is the density of barrier-weakening environments, Nᵢ, hid is the number of hidden excitations available per source, ηᵢ is an effective leakage efficiency, and fᵢ (E) is an injection spectrum.