#!/usr/bin/env python3 """ The 420 Code — the wave of September 2026: the four frozen results of the cost family and the Assembly, recomputed from CODATA 2022 at 50 digits. python3 verify_family.py Reproduces, to every printed digit: AP44 the realised gravitational constant (KS-CCC.3) 2026-09-04-G-KS-CCC.3.md AP47 the neutron-proton difference, realised (KS-FLIP.1) 2026-09-04-neutron-KS-FLIP.1.md AP46 the age of everything, one cycle (KS-STRETCH.3) 2026-09-04-age-KS-STRETCH.3.md AP48 the expansion rate, the closure (KS-ASM.1) 2026-09-04-H0-KS-ASM.1.md and the two corpses beside them (KS-NPP.1, KS-45.1), shown, never repaired. The one external dependency is mpmath (pip install mpmath). Copyleft 2026. Don't be a cunt. Be kind. """ from mpmath import mp, mpf, pi, sqrt, log, exp, cos, tan, asinh mp.dps = 50 # ── Inputs: CODATA 2022 (NIST) ──────────────────────────────────────────────── AINV = mpf('137.035999177') # 1/alpha ALPHA = 1 / AINV HBAR = mpf('1.054571817e-34') # J s, exact C = mpf('299792458') # m/s, exact M_E = mpf('9.1093837139e-31') # kg G_MEAS = mpf('6.67430e-11') # N m^2 kg^-2 (CODATA 2018, unchanged 2022) MP_ME = mpf('1836.152673426') MN_ME = mpf('1838.68366200') DELTA_U = mpf('7.4e-7') # 1-sigma bar on m_n/m_e - m_p/m_e KM_PER_MPC = mpf('3.0857e19') GYR = mpf('365.25') * 86400 * mpf('1e9') def s(x, n): return mp.nstr(x, n, strip_zeros=False) out = [] P = out.append # ── AP44: the realised G ───────────────────────────────────────────────────── alpha_G = ALPHA**21 * (1 + 1/pi) G_struct = alpha_G * HBAR * C / M_E**2 G_real = G_struct / (1 + ALPHA) P('AP44 — THE SNAP: the gravitational constant, realised (KS-CCC.3)') P(' alpha_G = alpha^21 (1 + 1/pi) = ' + s(alpha_G, 8)) P(' G_struct = alpha_G hbar c / m_e^2 = ' + s(G_struct, 6) + ' (AP28, provisioned: ' + s((G_struct/G_MEAS - 1)*100, 3) + ' %)') P(' 1/(1 + alpha) = ' + s(1/(1+ALPHA), 7)) P(' G_real = G_struct / (1 + alpha) = ' + s(G_real, 6) + ' (' + s((G_real/G_MEAS - 1)*100, 3) + ' % against CODATA ' + s(G_MEAS, 5) + ')') P(' the fork (KS-CCC.3): the adjusted value migrates toward 6.672e-11, or stays at 6.6743e-11 and the commitment dies.') P('') # ── AP47: the neutron, realised — and the corpse ───────────────────────────── d_bare = 3*(1 - 1/(2*pi)) + ALPHA*(1 + 1/(2*pi)) f2 = ALPHA**2 / (8*pi) d_real = d_bare / (1 + f2) d_meas = MN_ME - MP_ME P('AP47 — THE FLIP: the neutron-proton mass difference, realised (KS-FLIP.1)') P(' delta_bare = 3(1 - 1/2pi) + alpha(1 + 1/2pi) = ' + s(d_bare, 9) + ' [KS-NPP.1: FIRED 2026-08-02 at ' + s((d_bare - d_meas)/DELTA_U, 3) + ' sigma — shown, never repaired]') P(' f2 = alpha^2 / (8 pi) = ' + s(f2, 6)) P(' delta_real = delta_bare / (1 + f2) = ' + s(d_real, 12)) P(' measured (CODATA 2022 ratio difference) = ' + s(d_meas, 10) + ' +/- ' + s(DELTA_U, 2) + ' (0.29 ppm)') P(' residual = ' + s((d_real - d_meas)/DELTA_U, 2) + ' sigma') P(' KS-FLIP.3: the absent alpha^3 term would sit at ' + s(d_bare*ALPHA**3/(8*pi), 2) + ' m_e — ' + s(d_bare*ALPHA**3/(8*pi)/DELTA_U*100, 2) + ' % of the bar; adjudication waits on ~20x better B_d metrology.') P('') # ── AP46: the cycle ────────────────────────────────────────────────────────── tau_C = HBAR / (M_E * C**2) escape = ALPHA**-18 * tau_C t_cycle = escape * 21 / 18 lane = t_cycle / 21 AGE_MEAS, AGE_U = mpf('13.787'), mpf('0.020') P('AP46 — THE STRETCH: the age of everything, one cycle (KS-STRETCH.3)') P(' tau_C = hbar / (m_e c^2) = ' + s(tau_C, 11) + ' s (the tick)') P(' alpha^-18 ticks = ' + s(ALPHA**-18, 6)) P(' alpha^-18 tau_C (the thread) = ' + s(escape, 5) + ' s = ' + s(escape/GYR, 5) + ' Gyr') P(' x 21/18 (the duty) = ' + s(t_cycle/GYR, 5) + ' Gyr (one cycle)') P(' measured age (Planck 2018) = ' + s(AGE_MEAS, 5) + ' +/- ' + s(AGE_U, 2) + ' Gyr; landing ' + s((t_cycle/GYR/AGE_MEAS - 1)*100, 2) + ' %') P(' the lane (cycle/21) = ' + s(lane/GYR, 4) + ' Gyr; the window ' + s((t_cycle - lane)/GYR, 4) + ' to ' + s((t_cycle + lane)/GYR, 4) + ' Gyr') P('') # ── AP48: the closure ──────────────────────────────────────────────────────── f_DM_dark = (mpf(6)/21) * (1 - exp(-mpf(21)/6)) f_DE = (1 - f_DM_dark) * 20/21 f_DM = f_DM_dark * 20/21 f_vis = mpf(1)/21 om_L, om_m = f_DE, f_DM + f_vis H0t0 = (2/(3*sqrt(om_L))) * asinh(sqrt(om_L/om_m)) H0 = H0t0 / t_cycle * KM_PER_MPC H0_lo = H0t0 / (t_cycle + lane) * KM_PER_MPC H0_hi = H0t0 / (t_cycle - lane) * KM_PER_MPC settled = H0 * sqrt(om_L) Lam = 3 * (settled / KM_PER_MPC)**2 / C**2 P('AP48 — THE ASSEMBLY: the expansion rate, the closure (KS-ASM.1)') P(' Omega_L, Omega_m (AP42, the corpus\'s count) = ' + s(om_L, 5) + ', ' + s(om_m, 5)) P(' H0 t0 = (2/(3 sqrt(Omega_L))) asinh sqrt(Omega_L/Omega_m) = ' + s(H0t0, 5) + ' (the pure number)') P(' 1 / cycle = ' + s(KM_PER_MPC / t_cycle, 5) + ' km/s/Mpc') P(' H0 = H0t0 / cycle = ' + s(H0, 5) + ' km/s/Mpc; window ' + s(H0_lo, 4) + ' to ' + s(H0_hi, 4)) P(' Planck 2018 (TT,TE,EE+lowE+lensing) = 67.4 +/- 0.5; Cepheid ladder (JWST, SH0ES) 73.49 +/- 0.93 — outside the window') P(' settled rate = H0 sqrt(Omega_L) = ' + s(settled, 4) + ' km/s/Mpc = ' + s(settled/(KM_PER_MPC/t_cycle), 4) + ' of the cycle\'s inverse') P(' Lambda = 3 H_inf^2 / c^2 = ' + s(Lam, 4) + ' m^-2 (the same closure in other units)') P('') # ── The floor at the corpus's rate; the corpse of 74.3 ─────────────────────── CS2 = 2*log(1/cos(mpf('0.5')) + tan(mpf('0.5'))) a0 = CS2 * C * (H0/KM_PER_MPC) / (2*pi) A0_MEAS = mpf('1.20e-10'); A0_U = sqrt(mpf('0.02e-10')**2 + mpf('0.24e-10')**2) P('AP18 — THE FLOOR at the corpus\'s rate, and the corpse of KS-45.1') P(' C_S^2 = 2 ln(sec 1/2 + tan 1/2) = ' + s(CS2, 11)) P(' a0 = C_S^2 c H0 / (2 pi) at H0 = ' + s(H0, 4) + ' = ' + s(a0, 5) + ' m/s^2') P(' empirical scale = 1.20e-10 +/- 0.02 (random) +/- 0.24 (systematic): ' + s((A0_MEAS - a0)/A0_U, 2) + ' sigma low (' + s((1 - a0/A0_MEAS)*100, 2) + ' %)') P(' KS-45 (the coefficient 0.1662 vs the sky\'s 0.183 +/- 0.037): ' + s((A0_MEAS/(C*H0/KM_PER_MPC) - CS2/(2*pi))/mpf('0.037'), 2) + ' sigma — live') P(' KS-45.1 as registered: 74.3 +/- 1.2; (74.3 - H0)/1.2 = ' + s((mpf('74.3') - H0)/mpf('1.2'), 3) + ' sigma — FIRED 2026-09-03, shown, never repaired') P(' honest width of the inversion: 74.3 +/- ' + s(mpf('74.3') * mpf('0.24')/mpf('1.20'), 3) + ' (the registered +/- 1.2 omitted the systematic)') P('') P('One measured input (alpha). Zero free parameters. Two corpses on the board.') if __name__ == '__main__': print('\n'.join(out))