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(-S_BH/2)) gives Δf → 0 — undetectable — because S_BH ~ 10^78 for stellar-mass black holes makes ε effectively zero. Model A (Planck-scale surface, ε = l_Pl/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.