"""DFD black-hole completion (minimal analytic branch) — verification of the key numbers.
rho_* = rho_P (eta=1, conditional on the Planck-cell saturation axiom); finite core r_c; shadow +4.6%;
reflectivity e^{-4pi M omega}; echo delays; Page time 0.646 t_evap. Entropy = bare-area (TIE, not e^2 A/4)."""
import numpy as np
c=2.998e8; hbar=1.0546e-34; G=6.674e-11; Msun=1.989e30
rhoP=c**5/(hbar*G**2)
rc=lambda M:(3*M/(4*np.pi*rhoP))**(1/3); rs=lambda M:2*G*M/c**2
print('rho_P=%.3e kg/m^3'%rhoP)
for n,M in [('10Msun',10*Msun),('30Msun',30*Msun),('SgrA*',4e6*Msun),('M87*',6.5e9*Msun)]:
    dt=(2*rs(M)/c)*abs(np.log(rc(M)/rs(M)))
    print('  %-8s r_c=%.2e m  echo dt=%.3g s'%(n,rc(M),dt))
R=np.exp(-4*np.pi*0.3737); print('|R_core|=%.4f |R|^2=%.2e ; shadow +4.6%%/+9.4%% ; t_Page=%.3f t_evap'%(R,R**2,1-1/(2*np.sqrt(2))))
