# SCRIPT: RS03C_LINEAR_LIMIT
# After W2/W2b: the Richardson criterion failed because the error is a complex number whose phase
# turns with w, so a scalar power-law extrapolation of r misfires. This run asks the direct question:
# does |r(w) - Gamma| / (omega w) settle to a constant as w -> 0 (first-order convergence to Gamma)?
# Kill: the ratio changes by more than 2% between the last two widths at any angle.
import rs03_push_lib as L
ok = True
for th in [10, 25, 31, 60]:
    out = []
    for ow in [0.01, 0.005, 0.0025, 0.00125]:
        r, C = L.refl_resolved('tanh', 4, 1, 1, 0.5, ow/10, th); e = abs(r - L.gamma_pred(4, 1, C)); out.append(e/ow)
    ok &= abs(out[-1]/out[-2] - 1) < 0.02
    print(f"theta {th}: |r - Gamma|/(omega w) = " + ", ".join(f"{x:.4f}" for x in out) + "  at omega w = 0.01, 0.005, 0.0025, 0.00125", flush=True)
print('RS03C:', 'PASS (first-order convergence to Gamma)' if ok else 'KILL')