#!/usr/bin/env python3 """ verify_P049.py -- Addendum 49: W/Z masses from E6 adjoint sector. This verifier checks the Killing-form arithmetic, Weinberg-angle ratio, VEV cross-check, and W/Z closure table in 49_Addendum_WZMasses.tex. Most headline numerics reproduce and the paper correctly leaves the absolute W mass open. The flagged issues are a stale M_Z-from-M_W table value, an unverified "systematic scan" claim, a speculative RG attribution, and a TeX/math notation bug where \\sinW is defined as sin^2(theta_W) but used as sin(theta_W) in mixing generator formulas. """ from __future__ import annotations import math import sys from pathlib import Path sys.path.insert(0, str(Path(__file__).resolve().parent)) class Verifier: """Output shim: identical tolerance semantics to verify_common.Verifier, modern [PASS]/[FAIL] check-line output format.""" def __init__(self, name): self.PASS = 0 self.FAIL = 0 self.n = 0 print(name) def _mark(self, ok, desc): self.n += 1 if ok: self.PASS += 1 else: self.FAIL += 1 print(f" [{'PASS' if ok else 'FAIL'}] {self.n:>2}. {desc}") 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}%" self._mark(ok, label + (f" -- {detail}" if detail else "")) print(f" computed: {computed} claimed: {claimed} ({err_detail})") return ok def record(self, label, ok, computed="", claimed="", detail=""): ok = bool(ok) self._mark(ok, label + (f" -- {detail}" if detail else "")) if computed != "" or claimed != "": print(f" computed: {computed} claimed: {claimed}") return ok def summary(self): print(f"\n{'='*60}\nRESULT: {self.PASS} PASS / {self.FAIL} FAIL") return 0 if self.FAIL == 0 else 1 v = Verifier("P049 -- W/Z Masses from E6 Adjoint") ROOT = Path(__file__).resolve().parents[1] TEX = (ROOT / "49_Addendum_WZMasses.tex").read_text() PI = math.pi MU0 = 4 * PI**3 + PI**2 + PI MU1 = 16 * PI**3 / 5 + 3 * PI**2 / 4 + 2 * PI / 3 MU = MU1 / MU0 ME_GEV = 0.000511 MW = 80.377 MZ = 91.188 MH = 125.25 V_SM = 246.22 def pct(value: float, target: float) -> float: return 100 * (value - target) / abs(target) sin2_toe = 1 / (1 + PI) cos_toe = math.sqrt(PI / (1 + PI)) lambda_h = 9 * PI**2 / (5 * MU0) v_from_higgs = MH / math.sqrt(2 * lambda_h) g_toe2 = 4 * PI * (1 + PI) / MU0 g_toe = math.sqrt(g_toe2) g_sm = 2 * MW / v_from_higgs ew_killing = PI + math.log(12) / MU mw_killing_mev = ME_GEV * math.exp(MU * (ew_killing - PI)) * 1000 ew_obs = PI + math.log(MW / ME_GEV) / MU v.check("mu0", MU0, 137.036, rel=3e-6) v.check("mu1", MU1, 108.717, rel=5e-6) v.check("MU", MU, 0.79334, rel=3e-6) v.check("lambda_H=9pi^2/(5mu0)", lambda_h, 0.12964, rel=5e-5) v.check("sin^2 theta_W TOE", sin2_toe, 0.2415, rel=2e-4) v.check("cos theta_W TOE", cos_toe, 0.8709, rel=6e-5) v.check("Killing contribution total", 3 + 9 / 2 + 9 / 2, 12, rel=1e-12) v.check("Killing energy pi+ln(12)/MU", ew_killing, 6.27, rel=7e-4) v.check("Killing mass scale", mw_killing_mev, 6.0, rel=3e-2) v.check("observed W energy", ew_obs, 18.22, rel=3e-4) ratio_toe = 1 / cos_toe ratio_obs = MZ / MW v.check("mZ/mW TOE ratio", ratio_toe, 1.1482, rel=3e-5) v.check("observed mZ/mW ratio", ratio_obs, 1.1345, rel=4e-6) v.check("mZ/mW residual percent", pct(ratio_toe, ratio_obs), 1.21, rel=5e-3) v.check("mW from mZ and TOE theta", MZ * cos_toe, 79.42, rel=5e-5) v.check("mW-from-mZ residual", pct(MZ * cos_toe, MW), -1.19, rel=1e-2) v.check( "mZ from mW and TOE theta table row", MW / cos_toe, 91.09, rel=5e-4, detail="Expected fail: using observed mW and TOE theta gives about 92.29 GeV, not 91.09.", ) v.check( "mZ-from-mW residual table row", pct(MW / cos_toe, MZ), 1.1, rel=5e-2, detail="Expected fail: exact residual is about +1.21%, and the listed 91.09 is stale.", ) v.check("VEV from Higgs self-coupling and observed mH", v_from_higgs, 245.98, rel=2e-5) v.check("VEV residual percent", pct(v_from_higgs, V_SM), -0.10, rel=2e-2) v.check("g_SM from observed W and computed v", g_sm, 0.6535, rel=6e-5) v.check("g_TOE^2 candidate", g_toe2, 0.3798, rel=4e-5) v.check("g_TOE candidate", g_toe, 0.6163, rel=5e-5) v.check("mW from g_TOE and v", g_toe * v_from_higgs / 2, 75.79, rel=7e-5) v.check("mW g_TOE residual", pct(g_toe * v_from_higgs / 2, MW), -5.7, rel=4e-3) v.record( "systematic no-match scan is reproducible from the paper", False, computed="paper states a systematic scan but gives no candidate set, code, or result table", claimed="no algebraic combination maps Killing norm to E_W within 5%", detail="Expected verification gap.", ) v.record( "5.7 percent g deficit is derived from a TOE RG calculation", False, computed="paper gives only an order-of-magnitude one-loop estimate with typical GUT parameters", claimed="deficit attributable to RG running", detail="Expected status fail: plausible interpretation, not a computed derivation.", ) v.record( "mixing generator formulas use sin(theta), not sin^2(theta)", "\\newcommand{\\sinW}{\\sin^2\\!\\theta_W}" not in TEX or "Z^0 = \\cosW\\, W^3 - \\sinW\\, B" not in TEX, computed="\\sinW macro is sin^2(theta_W), but Z^0 and photon generator formulas use \\sinW as a linear mixing coefficient", claimed="Z^0 = cos(theta) W^3 - sin(theta) B", detail="Expected notation/formula fail.", ) v.record( "absolute W mass is explicitly open", "Conjecture 7.1 & \\textbf{Open (refined)}" in TEX and "$m_W$ absolute: requires RG calculation" in TEX, computed="status table leaves absolute mass open", claimed="ratio closed; absolute scale open", ) sys.exit(v.summary())