#!/usr/bin/env python3 """ verify_P084.py -- Addendum 84: Unified Quark Mass Table. This verifier recomputes the constants, spectral energies, quark masses, residuals, RMS residual, and selected mass-ratio claims in 84_Addendum_QuarkMassTable.tex. It intentionally fails the internally inconsistent top-mass table claim: the paper's own formula E_t = pi^2 + pi + ln(mu0)/MU gives m_t ~= 176.10 GeV, not 172.4 GeV. The abstract's older "+2.0%" top result is consistent with the formula; the later "172.4 GeV / -0.2%" recomputation is not. """ import math import sys from pathlib import Path PASS = FAIL = 0 _N = 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}") return ok class Verifier: """Target-style output adapter; check/record numerics are unchanged.""" 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_detail = f"abs err={abs(computed - claimed):.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=""): global _N ok = bool(ok) desc, extra = label, detail if not ok and detail: desc, extra = f"{label} -- {detail}", "" _N += 1 check(_N, desc, ok) if computed != "" or claimed != "": print(f" computed: {computed}") print(f" claimed : {claimed}") if extra: print(f" {extra}") return ok def summary(self): print(f"\n{'='*60}\nRESULT: {PASS} PASS / {FAIL} FAIL") return 1 if FAIL else 0 v = Verifier("P084 -- Unified Quark Mass Table") PI = math.pi M_E = 0.511 # MeV, as used in the paper. MU0 = 4 * PI**3 + PI**2 + PI MU1 = 16 * PI**3 / 5 + 3 * PI**2 / 4 + 2 * PI / 3 MU = MU1 / MU0 LAM = math.sin(PI / 14) PDG = { "u": 2.16, "d": 4.67, "s": 93.4, "c": 1270.0, "b": 4180.0, "t": 172_760.0, } E = { "u": PI ** (7 / 5), "d": math.log(MU1) / MU, "s": PI**2 - 1 / 7, "c": PI**2 + PI, "b": PI ** (7 / 3), "t": PI**2 + PI + math.log(MU0) / MU, } def mass_from_e(e): return M_E * math.exp(MU * (e - PI)) def e_from_mass(m): return PI + math.log(m / M_E) / MU def residual_pct(pred, actual): return 100 * (pred - actual) / actual v.check("mu0 = 4*pi^3 + pi^2 + pi", MU0, 137.036304, rel=5e-9) v.check("mu1 = 16*pi^3/5 + 3*pi^2/4 + 2*pi/3", MU1, 108.716684, rel=5e-9) v.check("MU = mu1/mu0", MU, 0.793342, rel=5e-7) v.check("lambda = sin(pi/14)", LAM, 0.222520, rel=5e-6) claimed_empirical_e = { "u": 4.9582, "d": 5.9309, "s": 9.7073, "c": 12.9963, "b": 14.4979, "t": 19.1869, } for q, claimed in claimed_empirical_e.items(): v.check(f"E_{q} empirical from PDG mass", e_from_mass(PDG[q]), claimed, rel=2e-4) claimed_spectral_e = { "u": 4.9672, "d": 5.9114, "s": 9.7267, "c": 13.0112, "b": 14.455, "t": 19.2131, } for q, claimed in claimed_spectral_e.items(): v.check(f"E_{q} TOE spectral formula", E[q], claimed, rel=4e-4) claimed_masses = { "u": 2.173, "d": 4.600, "s": 95.2, "c": 1287.0, "b": 4046.0, # The table states 172.4 GeV; the formula gives about 176.1 GeV. "t_table_late_GeV": 172.4, # The abstract / Addendum 45 value is formula-consistent. "t_formula_GeV": 176.1, } pred_mass = {q: mass_from_e(E[q]) for q in E} for q in ["u", "d", "s", "c", "b"]: tol = 5e-3 if q == "s" else 3e-3 v.check(f"m_{q} from spectral formula", pred_mass[q], claimed_masses[q], rel=tol) v.check( "m_t from spectral formula agrees with 176.1 GeV formula value", pred_mass["t"] / 1000, claimed_masses["t_formula_GeV"], rel=5e-4, ) v.check( "m_t from spectral formula vs late table claim 172.4 GeV", pred_mass["t"] / 1000, claimed_masses["t_table_late_GeV"], rel=5e-3, detail="Expected fail: late P84 recomputation/table uses inconsistent exponent arithmetic.", ) claimed_residuals = { "u_table": 0.6, "d_table": -1.5, "s_table": 1.9, "c_table": 1.3, "b_table": -3.2, "t_abstract": 2.0, "t_late_table": -0.2, } actual_residuals = {q: residual_pct(pred_mass[q], PDG[q]) for q in E} v.check("u residual vs PDG", actual_residuals["u"], claimed_residuals["u_table"], rel=2e-1) v.check("d residual vs PDG", actual_residuals["d"], claimed_residuals["d_table"], rel=1e-1) v.check("s residual vs PDG", actual_residuals["s"], claimed_residuals["s_table"], rel=2e-1) v.check("c residual vs PDG", actual_residuals["c"], claimed_residuals["c_table"], rel=1e-1) v.check("b residual vs PDG", actual_residuals["b"], claimed_residuals["b_table"], rel=1e-1) v.check("t residual matches abstract +2.0% value", actual_residuals["t"], claimed_residuals["t_abstract"], rel=5e-2) v.check( "t residual vs late table -0.2% claim", actual_residuals["t"], claimed_residuals["t_late_table"], rel=5e-1, detail="Expected fail: same inconsistency as m_t table value.", ) rms = math.sqrt(sum(x * x for x in actual_residuals.values()) / len(actual_residuals)) v.check("RMS residual over six quarks", rms, 2.0, rel=1e-1) v.check("m_d/m_u Weyl-step formula", math.exp(2 * MU * LAM**2 * PI**2), 2.17, rel=2e-3) v.check("PDG m_d/m_u ratio", PDG["d"] / PDG["u"], 2.16, rel=2e-3) v.check("m_s/m_mu = exp(-MU/7)", math.exp(-MU / 7), 0.8927, rel=5e-4) v.check("m_b/m_t formula ratio", math.exp(MU * (E["b"] - E["t"])), 0.02293, rel=1e-3) v.check("m_t/m_c = mu0", MU0, 137.036, rel=3e-6) v.check("PDG m_t/m_c ratio", PDG["t"] / PDG["c"], 136.03, rel=2e-5) v.check("m_s/m_d formula ratio", math.exp(MU * (E["s"] - E["d"])), 20.61, rel=3e-3) v.check("m_b/m_s formula ratio", math.exp(MU * (E["b"] - E["s"])), 42.43, rel=4e-3) sys.exit(v.summary())