#!/usr/bin/env python3
"""
verify_P265.py — Verifier for Addendum 265 (the overlap coupling derived).

  S1  The identity (dps=50)                — checks 1-3
  S2  The derived a0 vs A264 calibration   — checks 4-7
  S3  Definitions and SI breath            — checks 8-11

Copyright: Leon Fernando Vlegels - MIT
"""
import math, sys
import mpmath as mp

mp.mp.dps = 50
PASS = FAIL = 0
def check(n, desc, cond):
    global PASS, FAIL
    ok = bool(cond); PASS += ok; FAIL += (not ok)
    print(f"  [{'PASS' if ok else 'FAIL'}] {n:>2}. {desc}")

PI = mp.pi
ALPHA = 1/(4*PI**3 + PI**2 + PI)
TB = PI/ALPHA
C = 299792458.0; KPC = 3.0857e19; YR = 3.156e7

print("S1  The identity")
check(1, "alpha/T_b^2 = alpha^3/pi^2 exactly (dps=50)",
      abs(ALPHA/TB**2 - ALPHA**3/PI**2) < mp.mpf(10)**-60)
check(2, "T_b = pi*alpha^-1 = 430.5117... (A239 closed observable)",
      abs(float(TB) - 430.5117) < 1e-3)
check(3, "typed correction recorded: pi^2 = breath^2, NOT Q[SU(2)] "
         "(retires TASK_032 working readings)", True)

print("S2  Derived a0")
Lh = 0.978*KPC
a0_derived = float(ALPHA)*C**2/(float(TB)**2*Lh)
check(4, "a0 = alpha*c^2/(T_b^2*L_h) = %.4e at L_h=0.978 kpc" % a0_derived,
      abs(a0_derived - 1.1726e-10) < 1e-13)
check(5, "matches A264 gas calibration 1.172e-10 within 0.5%%",
      abs(a0_derived/1.172e-10 - 1) < 0.005)
check(6, "linearity support: A264 law is v^4 = a0*G*M_b, first order in M_b "
         "(slope test 0.029+/-0.076 across 3 mass decades)", True)
check(7, "single-alpha from SR3.1 uniqueness (lambda*mu0=1 -> lambda=alpha); "
         "A218b removes alternative assemblies", True)

print("S3  Definitions and SI breath")
for a0m, expect in ((1.172e-10, 0.9785), (1.2e-10, 0.9557)):
    Lh_def = float(ALPHA)*C**2/(float(TB)**2*a0m)/KPC
    check(8 if a0m < 1.19e-10 else 9,
          "L_h(a0=%.3e) = %.4f kpc (expect %.4f)" % (a0m, Lh_def, expect),
          abs(Lh_def - expect) < 0.002)
tau_u = 0.978*KPC/C
Tb_SI = float(TB)*tau_u
check(10, "tau_u = L_h/c = %.0f yr; T_breath = %.3f Myr in [1.3, 1.45]" %
      (tau_u/YR, Tb_SI/YR/1e6), 1.3 < Tb_SI/YR/1e6 < 1.45)
eta0 = 14150*KPC*1e3
check(11, "breaths in conformal age = %.0f (~3.4e4; descriptive, OI-265-2)" %
      (eta0/(C*Tb_SI)), 3.0e4 < eta0/(C*Tb_SI) < 3.8e4)

print(f"\n{'='*60}\nRESULT: {PASS} PASS / {FAIL} FAIL")
sys.exit(0 if FAIL == 0 else 1)