Time as Residual Thickness Numerical Definition of Time from Retention Rate λ

The Residual Principle (Sanada, 2026) established that a dimensionless retention rate λ ≈ 0.68 appears across unrelated domains: social hierarchy (0.682), galactic rotation (0.687), and thermal conduction (0.68). This paper extends that finding in two directions. First, the galactic vortex equation A_t = β(1 − e^(−r/R_ret)) is extended to r → 0. Structural prediction from the generative cycle (I → Δ → M → V → I’) yields: the center is not a singularity but a re-crossing gradient limit, and complete closure is impossible because dispersion (V) is present in the cycle. The equation confirms both: A_t(0) = 0 (generation does not close at the center) and A_t’(0) → ∞ as R_ret → 0 (the re-crossing gradient diverges). Prediction and equation arrive at the same point independently. Second, λ is shown to obey λ = e^(−kt), yielding the numerical definition of time: t = −ln(λ)/k. Time is not clock progression but the cumulative thickness of interference history readable from residual structure.