Topological Origin of Flavor Mixing and the Cabibbo Scale via Exact Path Integrals (Information-Geometric Physics System IV)

This paper develops the Information-Geometric Physics System (IGPS) as an effective field-theoretic framework in which gauge structure and flavor hierarchy emerge from the geometry and topology of seam configurations. Key Findings: Emergence of SU (3) Symmetry: Gauge structure is not introduced as a fundamental input; rather, the minimal non-trivial seam configuration uniquely leads to an SU (3) gauge group via representations of the fundamental group. Effective Transverse Potential: The framework derives an effective radial potential V₄₅₅ (r) = (u/2) r² - N₄₅₅ r directly from the extrinsic curvature of the seam. Exact Path Integrals: The partition function over the CP² moduli space integrates exactly to Z (u) u^-p, yielding a half-renormalized exponent p = (M + N₄₅₅) /2. Parameter-Free Cabibbo Scale Prediction: Without ad hoc phenomenological parameter fitting, the ground-state expectation value predicts ₈₆₏ₒ 0. 2248. This is numerically within 0. 14% of the observed Cabibbo parameter |Vₔₒ| = 0. 2245 0. 0008. Flavor Mixing Structure: Mixing matrix elements naturally arise from spatial overlap integrals of seam-localized modes, structurally reproducing the Wolfenstein hierarchy in the localized regime. Open Problems & Physical Justifications: The exact prediction of ₈₆₏ₒ is conditional on two formal conjectures outlined in the paper: Born-Infeld UV Matching and the u_ = 1 Bound: The value u_ = 1 is not an arbitrary assumption. It is identified as the unique internally consistent value through a three-sided argument. The Born-Infeld field-strength bound requires u 1 so that the vortex core field does not exceed the UV cutoff. Conversely, the seam EFT validity condition requires u 1 so that the UV cutoff does not resolve inside the vortex core. These boundaries strictly pin u = 1 as the only self-consistent value. The remaining open problem is formally deriving the required identity ₔₕ = gc v from a UV completion of the non-Abelian Born-Infeld action. Spectral Defect Reduction Conjecture: Translating the WZW edge central charge c₄₃₆₄ = 2 into the required entropic shift depends on the relation ₁₀ₑ₄ = c₄₃₆₄/ (6). While this is geometrically supported by internal consistency checks (such as the codimension-2 Poisson equation argument), it awaits a complete rigorous proof.