This document rewrites and consolidates the core mathematical content of "The Universal Boundary — Volume I (λ = 2)" by integrating the Finite-Sample Ratio Estimator (FSRE) framework from "FSRE-CANLE: A Unified Framework for Non-Linear Sensitivity Analysis". The result is a single, testable structure: (i) an exact boundary theorem for the second-order recurrence aₙ = aₙ₋₁ + c aₙ₋₂ identifying the unique universally critical coefficient c = 2; (ii) the Jacobsthal sequence as the canonical boundary recurrence; and (iii) an FSRE estimation layer that recovers λ from finite data using ratio convergence, Aitken acceleration, and a robust convergence-rate diagnostic ρ. The integration separates exact recurrence theory from empirical claims, providing a falsifiable pipeline for any domain where ratios can be measured.