#!/usr/bin/env python3 """ verify_prereg.py — regenerates every number in 2026-08-02-mp-me-alpha3.md from CODATA 2022 inputs. No fitted quantities are used as input. pip install mpmath python3 verify_prereg.py Inputs are CODATA 2022 (NIST, physics.nist.gov/cuu/Constants, 2026-08-02). Copyleft 2026. Don't be a cunt. Be kind. """ from itertools import combinations_with_replacement from mpmath import mp, mpf, pi, sqrt mp.dps = 50 # ------------------------------------------------------------------ inputs AINV, AINV_U = mpf('137.035999177'), mpf('0.000000021') # CODATA 2022 MP_ME, MP_ME_U = mpf('1836.152673426'), mpf('0.000000032') MU_ME = mpf('206.7682827') ALPHA = 1 / AINV ALPHA_U = ALPHA * (AINV_U / AINV) ppt = lambda x: x / MP_ME * mpf(1e12) ppb = lambda x: x / MP_ME * mpf(1e9) s = lambda x, n=6: mp.nstr(x, n) def rule(title): print('\n' + title + '\n' + '-' * len(title)) # ------------------------------------------------------- §4 frozen value rule('SECTION 4 — the frozen O(alpha^2) value') T0 = mpf(21**2 * 4 + 21 * 3 + 3**2) T1 = ALPHA * 21 * (1 - 1 / (84 * pi)) T2 = ALPHA**2 * 21 * mpf(16) / 1836 D = T0 + T1 + T2 dD = 21 * (1 - 1 / (84 * pi)) + 2 * ALPHA * 21 * mpf(16) / 1836 D_U = dD * ALPHA_U U = sqrt(MP_ME_U**2 + D_U**2) resid = D - MP_ME print(f' 21^2*4 + 21*3 + 3^2 = {T0}') print(f' alpha*21*(1 - 1/(84*pi)) = {s(T1, 15)}') print(f' alpha^2*21*16/1836 = {s(T2, 15)}') print(f' D = {s(D, 16)}') print(f' u(D) propagated from alpha = {s(ppt(D_U), 3)} ppt') print(f' D - measured = +{s(ppt(resid), 4)} ppt (+{s(ppb(resid), 4)} ppb)') print(f' measurement uncertainty = {s(ppt(MP_ME_U), 4)} ppt') print(f' discrepancy = {s(resid / U, 3)} sigma') print(f' sign required of any alpha^3 term to close it: NEGATIVE') print(f' (alpha and alpha^2 terms are both positive)') # --------------------------------------------- §4a alpha^2 coefficient pinned rule('SECTION 4a — the alpha^2 coefficient is empirically pinned') c2 = (MP_ME - T0 - T1) / ALPHA**2 c2u = MP_ME_U / ALPHA**2 corpus_c2 = mpf(21) * 16 / 1836 print(f' required by measurement = {s(c2, 7)} +/- {s(c2u, 3)}') print(f' constraint = {s(c2u / c2 * 100, 3)} % of the value') print(f' corpus 21*16/1836 = {s(corpus_c2, 7)}') print(f' agreement = {s(abs(corpus_c2 - c2) / c2u, 3)} sigma') print(f' implied owed integer 16 = {s(c2 * 1836 / 21, 6)} +/- {s(c2u * 1836 / 21, 3)}') num, numu = c2 * 1836, c2u * 1836 print(f' numerator over 1836 = {s(num, 7)} +/- {s(numu, 3)}') lo, hi = int(mp.floor(num - 3 * numu)), int(mp.ceil(num + 3 * numu)) prods = {21**i * 3**j * 4**k for i in range(3) for j in range(7) for k in range(6) if 21**i * 3**j * 4**k <= 500} hits = [n for n in range(lo, hi + 1) if n in prods] print(f' integers in the 3-sigma window = {list(range(lo, hi + 1))}') print(f' ... that are products of 21,3,4 = {hits} <- 336 = 21x16 = 84x4 = 4^2x21') rank3 = mpf(21 * 64) / 1836 print(f' naive rank-3 continuation 4^3=64 -> c3 = {s(rank3, 5)}, which lands at ' f'{s(abs(D + rank3 * ALPHA**3 - MP_ME) / U, 3)} sigma -> EXCLUDED') print(' any derivation giving 16 at order 2 must NOT give 64 at order 3.') # --------------------------------------------------- §5 c3 is unconstrained rule('SECTION 5 — the order-3 coefficient is unconstrained') c3 = -resid / ALPHA**3 c3u = U / ALPHA**3 print(f' alpha^3 = {s(ALPHA**3, 8)}') print(f' c3 = -(D - measured)/alpha^3 = {s(c3, 4)} +/- {s(c3u, 4)} (1 sigma)') print(f' 1 sigma interval = [{s(c3 - c3u, 4)}, {s(c3 + c3u, 4)}]') print(f' uncertainty / |central| = {s(c3u / abs(c3), 3)}') hits, seen = 0, set() for a in range(-1, 3): for b in range(0, 3): for c in range(0, 3): for d in range(0, 3): for e in range(0, 3): for f in range(0, 3): v = (mpf(21)**a * mpf(3)**b * mpf(4)**c * mpf(6)**d / (mpf(1836)**e * pi**f)) for sg in (1, -1): cv = sg * v if abs(D + cv * ALPHA**3 - MP_ME) / U < 1: k = mp.nstr(cv, 12) if k not in seen: seen.add(k) hits += 1 print(f' bounded grammar +/-21^a 3^b 4^c 6^d / (1836^e pi^f), exponents in [-1,2]:') print(f' distinct admissible c3 values within 1 sigma = {hits}') rule(' named candidates (none of these is registered as a prediction)') for lab, cv in [('D series terminates, c3 = 0', mpf(0)), (' c3 = -1/21', -mpf(1) / 21), (' c3 = +1/21 (sign the stated rule implies)', mpf(1) / 21), (' c3 = -21*4/1836', -mpf(84) / 1836), (' c3 = -21*16/1836 (same-coefficient continuation)', -mpf(336) / 1836), (' c3 = +21*16/1836', mpf(336) / 1836), (' c3 = -21*64/1836 (rank-3 escalation)', -mpf(1344) / 1836)]: v = D + cv * ALPHA**3 print(f' {lab:46s} {s(v, 16)} {s(abs(v - MP_ME) / U, 3):>7s} sigma') # ------------------------------------------------ §6 uniqueness enumeration rule('SECTION 6 — decomposition enumeration') terms = {} for a in range(0, 3): for b in range(0, 8): for c in range(0, 6): v = 21**a * 3**b * 4**c if v <= 1836: terms.setdefault(v, (a, b, c)) vals = sorted(terms) c12 = [t for t in combinations_with_replacement(vals, 3) if sum(t) == 1836] order21 = lambda t: sorted(t, key=lambda x: terms[x][0], reverse=True) nfac = lambda x: sum(terms[x]) # structural factors, counted with multiplicity def cond3(t): # 21-exponent strictly decreasing e = [terms[x][0] for x in order21(t)] return e[0] > e[1] > e[2] def cond4(t): # factor count non-increasing: the hierarchy sheds f = [nfac(x) for x in order21(t)] return f[0] >= f[1] >= f[2] def show(t): d = order21(t) return (' + '.join(f'21^{terms[x][0]}*3^{terms[x][1]}*4^{terms[x][2]}' for x in d) + ' = ' + ' + '.join(str(x) for x in d) + ' factors ' + str([nfac(x) for x in d])) for lbl, sel in [('1+2 ', lambda t: True), ('1+2+3 ', cond3), ('1+2+4 ', cond4), ('1+2+3+4 ', lambda t: cond3(t) and cond4(t))]: r = [t for t in c12 if sel(t)] print(f' conditions {lbl}: {len(r)}') for t in r: print(' ', show(t)) print(f' \u00d8 Predictions reports 11 under 1+2 -> reproduced') print(f' \u00d8 Predictions reports 1 under 1+2+3 -> NOT reproduced (2)') print(f' condition 4 formalised 2026-08-02, after the alternative surfaced; see \u00a76') # ---------------------------------------------------------- §7 kill margins rule('SECTION 7 — when D dies, if the central value holds') for n in (3, 5): print(f' {n} sigma reached at measurement uncertainty <= {s(ppt(resid) / n, 3)} ppt') print(f' current: CODATA 2022 {s(ppt(MP_ME_U), 3)} ppt | HD+ 20.2 ppt | H2+ 25.6 ppt') # ----------------------------------------------------------------- §9 muon rule('SECTION 9 — the muon is below the construction floor') floor = 21**2 + 21 + 1 print(f' minimum three-term sum with strictly decreasing 21-exponents:') print(f' 21^2 * 1 + 21^1 * 1 + 21^0 * 1 = 441 + 21 + 1 = {floor}') print(f' m_mu/m_e = {MU_ME} < {floor}') print(f' unreachable at any exponents. The lepton sector is not derived.') print()