Axiomatic Extension of Gravitational Dynamics: Continuum Limit and Static Reduction of κ–τ Theory

This multi‑chapter release of the Infinite–Finite Cosmology series develops the κ–τ generator framework from its discrete lattice formulation through its continuum and static‑limit reductions. The chapters establish the coupled field equations for the torsion field κ and curvature field τ, derive their continuum wave‑equation structure, and obtain the radial ODEs governing the static, spherically symmetric sector. The analysis shows that τ(r)∼1/r while κ(r) varies slowly, producing an interaction term κ^2 * τ^2 ∝ 1/r^2 that acts as an effective density ρ_κτ(r)=σ/r^2 in the Poisson equation. This yields flat rotation curves with v^2=4πGσ. Together, these chapters provide the continuum‑limit, static‑limit, and radial‑equation machinery used throughout the subsequent development of the κ–τ generator field theory.