CCEGA Paper 23: Surface Position ε from Kerr Entropy — Robustness of the Δf(M, a*) Ratio Table

Constrains the CCEGA reflective surface position ε in Kerr geometry by evaluating two physically motivated models. Model B (entropy-suppressed surface, ε ~ exp (-SBH/2) ) gives Δf → 0 — undetectable — because SBH ~ 10⁷8 for stellar-mass black holes makes ε effectively zero. Model A (Planck-scale surface, ε = lPl/r_+) gives Δf ~ 10–100 Hz within the Einstein Telescope band. The spin-dependent correction to ln (1/ε) from the variation of r_+ with a* is less than 1% across the full spin range, confirming that the ratio table of Paper 22 is robust to better than 1%. The derivation of ε from the modulus field equation of motion in Kerr geometry is identified as the central open problem of the CCEGA black hole sector. All numbers independently verified.