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 $mathrm{SU}(3)$ Symmetry: Gauge structure is not introduced as a fundamental input; rather, the minimal non-trivial seam configuration uniquely leads to an $mathrm{SU}(3)$ gauge group via representations of the fundamental group. Effective Transverse Potential: The framework derives an effective radial potential $V_{mathrm{eff}}(r) = (u/2)r^2 - N_{mathrm{eff}}log r$ directly from the extrinsic curvature of the seam. Exact Path Integrals: The partition function over the $mathbb{CP}^2$ moduli space integrates exactly to $Z(u) propto u^{-p}$, yielding a half-renormalized exponent $p = (M + N_{mathrm{eff}})/2$. Parameter-Free Cabibbo Scale Prediction: Without ad hoc phenomenological parameter fitting, the ground-state expectation value predicts $lambda_{mathrm{IGPS}} approx 0.2248$. This is numerically within 0.14% of the observed Cabibbo parameter $|V_{us}| = 0.2245 pm 0.0008$. 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. (Truncated by ai.viXra,org Admin)