#!/usr/bin/env python3 """ verify_P100.py -- Addendum 100: Complete Standard Model synthesis table. This verifier checks the numerical consistency of the summary table in 100_Addendum_CompleteSM.tex. Most table entries reproduce if one uses the older corpus mass slope MU = (16*pi^3/5 + 3*pi^2/4 + 2*pi/3)/mu0. The paper's displayed P100 formula for MU, however, is a different expression and gives about 113, not 0.79334. """ import math import sys from pathlib import Path PASS = FAIL = 0 _N = 0 def check(desc, cond): global PASS, FAIL, _N _N += 1 ok = bool(cond) PASS += ok FAIL += not ok print(f" [{'PASS' if ok else 'FAIL'}] {_N:>2}. {desc}") return ok class Verifier: """Same check semantics as verify_common.Verifier; modern output style.""" def __init__(self, name): print(name) def check(self, label, computed, claimed, *, rel=1e-3, abs_tol=None, detail=""): if abs_tol is not None: ok = abs(computed - claimed) <= abs_tol err = abs(computed - claimed) err_detail = f"abs err={err:.6g}, tol={abs_tol:.6g}" else: if claimed == 0: ok = abs(computed) <= (rel or 1e-12) err_detail = f"abs value={abs(computed):.6g}, tol={rel:.6g}" else: err = (computed - claimed) / abs(claimed) ok = abs(err) <= (rel or 0) err_detail = f"rel err={100 * err:+.6g}%, tol={100 * (rel or 0):.6g}%" return self.record(label, ok, computed, claimed, err_detail + (f"; {detail}" if detail else "")) def record(self, label, ok, computed="", claimed="", detail=""): check(label + (f" -- {detail}" if detail else ""), ok) if computed != "" or claimed != "": print(f" computed: {computed}") print(f" claimed : {claimed}") return ok def summary(self): print(f"\n{'='*60}\nRESULT: {PASS} PASS / {FAIL} FAIL") return 1 if FAIL else 0 v = Verifier("P100 -- Complete Standard Model Synthesis") PI = math.pi M_E = 0.51100 MU0 = PI + PI**2 + 4 * PI**3 MU_DISPLAY = (PI**2 + PI**4 + 16 * PI**6) / MU0 MU_CORPUS = (16 * PI**3 / 5 + 3 * PI**2 / 4 + 2 * PI / 3) / MU0 LAM = math.sin(PI / 14) C_NLO = 1 - 4 * LAM**2 / 5 PHI_GOLDEN = (1 + math.sqrt(5)) / 2 SIN2_LO = 1 / (1 + PI) SIN2_NLO = SIN2_LO * C_NLO PHI_CKM = math.cos(PI / 14) * math.cos(2 * PI / 14) * math.cos(5 * PI / 28) A_LO = math.cos(PI / 14) ** 2 * math.cos(2 * PI / 14) A_NLO = A_LO * C_NLO DELTA = 31 * PI / 84 RHO = 0.5 * PHI_CKM * math.cos(DELTA) ETA = 0.5 * PHI_CKM * math.sin(DELTA) J_LO = A_LO**2 * LAM**6 * ETA J_NLO = J_LO * (1 - 48 * LAM**4 / 25) def mass_from_e(energy: float) -> float: return M_E * math.exp(MU_CORPUS * (energy - PI)) def residual(value: float, target: float) -> float: return 100 * (value - target) / target v.check("mu0 sector trace", MU0, 137.03630, rel=5e-8) v.check( "displayed MU formula equals stated 0.79334", MU_DISPLAY, 0.79334, rel=1e-3, detail="Expected fail: (pi^2 + pi^4 + 16*pi^6)/mu0 is about 113.03, not the mass slope.", ) v.check("corpus MU mass slope", MU_CORPUS, 0.79334, rel=5e-6) v.check("lambda = sin(pi/14)", LAM, 0.22252, rel=5e-6) v.check("4 lambda^2 / 5", 4 * LAM**2 / 5, 0.039612, rel=2e-5) v.check("C_NLO = 1 - 4lambda^2/5", C_NLO, 0.96039, rel=3e-6) v.check("Phi CKM calibration", PHI_CKM, 0.7437, rel=7e-5) v.check("A_LO", A_LO, 0.8564, rel=6e-5) v.check("A_NLO", A_NLO, 0.82243, rel=6e-6) v.check("sin^2 theta_W LO", SIN2_LO, 0.24145, rel=2e-5) v.check("sin^2 theta_W NLO", SIN2_NLO, 0.23189, rel=1e-5) v.check("sin^2 theta_W NLO residual percent", residual(SIN2_NLO, 0.23122), 0.29, rel=5e-3) v.check("sin^2 theta_W NLO / (3/8)", SIN2_NLO / (3 / 8), 0.61837, rel=3e-6) v.check("golden-ratio near-miss percent", abs(residual(SIN2_NLO / (3 / 8), 1 / PHI_GOLDEN)), 0.05, rel=1e-1) v.check("m_mu from pi^2", mass_from_e(PI**2), 106.30, rel=5e-5) v.check("m_mu residual percent", residual(mass_from_e(PI**2), 105.66), 0.60, rel=1e-2) v.check("m_tau from pi^2 + pi + 2/5", mass_from_e(PI**2 + PI + 2 / 5), 1765.0, rel=5e-5) v.check("m_tau residual percent", residual(mass_from_e(PI**2 + PI + 2 / 5), 1776.86), -0.67, rel=1e-2) v.check("m_u table", mass_from_e(PI ** (7 / 5)), 2.173, rel=1e-4) v.check("m_d table", mass_from_e(PI ** (14 / 9)), 4.683, rel=5e-5) v.check("m_s table", mass_from_e(PI**2 - 1 / 7), 94.9, rel=1e-4) v.check("m_b table", mass_from_e(PI ** (7 / 3)), 4039.8, rel=5e-5) v.check("m_t table", mass_from_e(PI**2 + PI + math.log(MU0) / MU_CORPUS), 176101, rel=5e-5) v.check("m_t residual percent", residual(mass_from_e(PI**2 + PI + math.log(MU0) / MU_CORPUS), 172690), 1.98, rel=2e-2) v.check("lambda_CKM table", LAM, 0.22252, rel=5e-6) v.check("lambda_CKM residual percent", residual(LAM, 0.22500), -1.10, rel=5e-3) v.check("A_NLO table", A_NLO, 0.82243, rel=6e-6) v.check("A_NLO residual percent", residual(A_NLO, 0.826), -0.43, rel=1e-2) v.check("rho_bar table", RHO, 0.14871, rel=1e-5) v.check("rho_bar residual percent", residual(RHO, 0.1472), 1.03, rel=1e-2) v.check("eta_bar table", ETA, 0.34084, rel=2e-5) v.check("eta_bar residual percent", residual(ETA, 0.3441), -0.95, rel=1e-2) v.check("J_LO", J_LO, 3.035e-5, rel=2e-4) v.check("J_NLO", J_NLO, 3.020e-5, rel=1e-4) v.check("J_NLO residual percent", residual(J_NLO, 3.08e-5), -1.94, rel=2e-2) theta12 = math.degrees(5 * PI / 28) theta23_ckm = A_NLO * LAM**2 theta23 = 45 - math.degrees(LAM**2 / 2) - math.degrees(theta23_ckm) theta13 = math.degrees(math.asin(LAM / math.sqrt(2) * (1 - 3 * LAM**2 / 4))) delta_pmns = -math.degrees(PI / 3 + PI / 28) v.check("theta12 PMNS", theta12, 32.14, rel=1e-4) v.check("theta12 residual percent", residual(theta12, 33.41), -3.79, rel=5e-3) v.check("theta23 PMNS", theta23, 41.25, rel=5e-5) v.check("theta23 residual percent", residual(theta23, 42.2), -2.26, rel=5e-3) v.record( "theta23 marked closed under <=2.1 percent criterion", abs(residual(theta23, 42.2)) <= 2.1, f"{residual(theta23, 42.2):+.4f}%", "<=2.1%", "Expected fail: table marks theta23 closed, but its listed residual is about 2.26%.", ) v.check("theta13 PMNS", theta13, 8.71, rel=5e-4) v.check("theta13 residual percent", residual(theta13, 8.57), 1.68, rel=5e-3) v.check("delta_CP PMNS magnitude residual percent", abs(residual(abs(delta_pmns), 66.0)), 0.65, rel=5e-3) m_h_nlo = 246.22 / 2 * math.sqrt(1 + 4 * LAM**2 / 5) v.check("m_H NLO", m_h_nlo, 125.52, rel=5e-5) v.check("m_H residual percent", residual(m_h_nlo, 125.20), 0.26, rel=1e-2) v.check("v = 2 * 123.11 GeV", 2 * 123.11, 246.22, rel=1e-12) v.check( "literal v = 2*m_H_NLO", 246.22, 2 * m_h_nlo, rel=1e-3, detail="Expected fail if the abstract's 'v = 2 m_H at all orders' is read literally; the theorem later uses m_H^LO.", ) mw_mz_ratio = math.sqrt(1 - SIN2_NLO) mw_from_displayed_expr = 91.1876 * mw_mz_ratio v.check("M_W/M_Z table ratio", mw_mz_ratio, 0.87642, rel=5e-6) v.check("M_W/M_Z residual percent", residual(mw_mz_ratio, 0.8815), -0.58, rel=2e-2) v.check( "M_W from displayed expression M_Z sqrt(1-sin^2 theta_W)", mw_from_displayed_expr, 77.42, rel=5e-4, detail="Expected fail: the displayed expression with PDG M_Z gives about 79.92 GeV; 77.42 is the separate P93 absolute tree value.", ) v.check("P93 absolute tree M_W residual percent", residual(77.42, 80.38), -3.68, rel=5e-3) listed_closed_residuals = [ residual(SIN2_NLO, 0.23122), residual(mass_from_e(PI**2), 105.66), residual(mass_from_e(PI**2 + PI + 2 / 5), 1776.86), residual(mass_from_e(PI ** (7 / 5)), 2.2), residual(mass_from_e(PI ** (14 / 9)), 4.7), residual(mass_from_e(PI**2 - 1 / 7), 93.0), residual(mass_from_e(PI**2 + PI + math.log(MU0) / MU_CORPUS), 172690), residual(LAM, 0.22500), residual(A_NLO, 0.826), residual(RHO, 0.1472), residual(ETA, 0.3441), residual(J_NLO, 3.08e-5), residual(theta12, 33.41), residual(theta23, 42.2), residual(theta13, 8.57), residual(abs(delta_pmns), 66.0), residual(m_h_nlo, 125.20), ] rms = math.sqrt(sum(x * x for x in listed_closed_residuals) / len(listed_closed_residuals)) v.check("RMS over reproducible listed residuals", rms, 1.54, rel=1e-2) v.record( "reproducible closed-observable count equals claimed 20", len(listed_closed_residuals) == 20, len(listed_closed_residuals), 20, "Expected fail/ambiguity: the 1.54% RMS reproduces over 17 listed central predictions, not an unambiguous set of 20.", ) sys.exit(v.summary())