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 Veff(r) = (u/2)r² - Nefflog 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 + Neff)/2. Parameter-Free Cabibbo Scale Prediction: Without ad hoc phenomenological parameter fitting, the ground-state expectation value predicts λIGPS ≈ 0.2248. This is numerically within 0.14% of the observed Cabibbo parameter |Vᵤₛ| = 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 λIGPS is conditional on two formal conjectures outlined in the paper: Born-Infeld UV Matching and the uₘᵢₙ = 1 Bound: The value uₘᵢₙ = 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 ΛUV = gc v from a UV completion of the non-Abelian Born-Infeld action. Spectral Defect Reduction Conjecture: Translating the WZW edge central charge cedge = 2 into the required entropic shift depends on the relation γbare = cedge/(6π). While this is geometrically supported by internal consistency checks (such as the codimension-2 Poisson equation argument), it awaits a complete rigorous proof.