#!/usr/bin/env python3 """ verify_P102.py -- Addendum 102: final NNLO Higgs closure. This verifier checks the nested-loop coefficient, the full c4 arithmetic, the Higgs mass prediction, and the target/tolerance logic. The final mass value is reproducible, but the claimed PDG-required c4 target is not the central-value closure coefficient for m_H = 125.20 GeV; it corresponds approximately to the lower edge of the 1-sigma band. """ import math import sys from pathlib import Path sys.path.insert(0, str(Path(__file__).resolve().parent)) from verify_common import CheckResult, Verifier class ModernVerifier(Verifier): """Local output adapter: tolerance logic byte-identical to verify_common.Verifier.check; emits the modern corpus line format (" [PASS] {n:>2}. {desc}") with computed/claimed/tolerance values kept as indented info lines, and the modern RESULT footer.""" def __init__(self, name: str): self.name = name self.results = [] self._n = 0 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._emit(label, ok, computed, claimed, err_detail, detail) def record(self, label, ok, computed="", claimed="", detail=""): return self._emit(label, ok, computed, claimed, "", detail) def _emit(self, label, ok, computed, claimed, info, ann): full_detail = (info + (f"; {ann}" if ann else "")) if info else ann self.results.append(CheckResult(label, ok, computed, claimed, full_detail)) self._n += 1 desc = f"{label} -- {ann}" if ann else label print(f" [{'PASS' if ok else 'FAIL'}] {self._n:>2}. {desc}") if computed != "" or claimed != "": print(f" computed: {computed}") print(f" claimed : {claimed}") if info: print(f" {info}") return ok def summary(self): passed = sum(bool(r.ok) for r in self.results) failed = len(self.results) - passed print(f"\n{'='*60}\nRESULT: {passed} PASS / {failed} FAIL") return 1 if failed else 0 v = ModernVerifier("P102 -- Final NNLO Higgs Closure") ROOT = Path(__file__).resolve().parents[1] TEX = (ROOT / "102_Addendum_HiggsNNLO_Final.tex").read_text() PI = math.pi V_EW = 246.22 M_H_PDG = 125.20 SIGMA_H = 0.11 LAM = math.sin(PI / 14) LAM2 = LAM**2 LAM4 = LAM**4 def higgs_mass_from_c4(c4: float) -> float: return (V_EW / 2) * math.sqrt(1 + 4 * LAM2 / 5 + c4 * LAM4) def rel_pct(value: float, target: float) -> float: return 100 * (value - target) / target v.check("lambda = sin(pi/14)", LAM, 0.22252, rel=5e-6) v.check("lambda^2", LAM2, 0.049516, rel=1e-5) v.check("lambda^4", LAM4, 0.0024518, rel=5e-5) v.check("4 lambda^2 / 5", 4 * LAM2 / 5, 0.039613, rel=2e-5) c4a = 16 / 25 c4b = 1 / 40 c4c = -18 / 5 c4_total = c4a + c4b + c4c v.check("topology a c4", c4a, 0.640, rel=1e-12) v.check("topology b c4 from claimed N=10", (1 / 16) * (4 / 10), 1 / 40, rel=1e-12) v.check("topology c c4", c4c, -3.600, rel=1e-12) v.check("full c4 = 16/25 + 1/40 - 18/5", c4_total, -587 / 200, rel=1e-12) v.check("full c4 decimal", c4_total, -2.935, rel=1e-12) v.check("gap to paper c4_req=-2.945", abs(c4_total - (-2.945)), 0.010, rel=1e-12) radicand = 1 + 4 * LAM2 / 5 + c4_total * LAM4 mass = higgs_mass_from_c4(c4_total) v.check("NNLO radicand", radicand, 1.032417, rel=1e-5) v.check("sqrt radicand", math.sqrt(radicand), 1.016081, rel=5e-6) v.check("NNLO Higgs mass", mass, 125.09, abs_tol=0.005) v.check("NNLO residual GeV", mass - M_H_PDG, -0.11, abs_tol=0.002) v.check("NNLO residual sigma", (mass - M_H_PDG) / SIGMA_H, -1.0, rel=1e-2) v.check("NNLO residual percent", rel_pct(mass, M_H_PDG), -0.09, rel=2e-2) v.record( "exact NNLO mass lies inside strict one-sigma interval", abs(mass - M_H_PDG) <= SIGMA_H, f"mass={mass:.9f}, lower={M_H_PDG - SIGMA_H:.9f}", "[125.09, 125.31]", "Expected fail: exact arithmetic is about 0.00052 GeV below the lower edge; rounded 125.09 is on the edge.", ) mass_p101 = higgs_mass_from_c4(-74 / 25) v.check("P101 a+c radicand", 1 + 4 * LAM2 / 5 - 74 * LAM4 / 25, 1.032356, rel=5e-6) v.check("P101 a+c mass", mass_p101, 125.09, abs_tol=0.01) v.check("P102 mass shift from topology b", mass - mass_p101, 0.004, abs_tol=0.001) v.check( "radicand shift from topology b is zero", c4b * LAM4, 0.0, abs_tol=1e-8, detail="Expected fail: including c4b=1/40 shifts the radicand by about 6.13e-5; the later text also states this correctly.", ) # PDG target coefficient and tolerance logic. target_factor_central = (2 * M_H_PDG / V_EW) ** 2 c4_req_central = (target_factor_central - (1 + 4 * LAM2 / 5)) / LAM4 mass_from_paper_req = higgs_mass_from_c4(-2.945) v.check( "PDG central target factor (2m/v)^2", target_factor_central, 1.03239, rel=5e-5, detail="Expected fail: 125.20 GeV gives about 1.03424; 1.03239 corresponds to a mass near 125.088 GeV.", ) v.check( "c4 required for PDG central mass", c4_req_central, -2.945, rel=5e-3, detail="Expected fail: exact central closure requires c4 about -2.19 in the signed convention used here.", ) v.check( "mass produced by paper c4_req=-2.945", mass_from_paper_req, M_H_PDG, abs_tol=SIGMA_H / 10, detail="Expected fail: c4=-2.945 gives about 125.088 GeV, the lower edge of the 1-sigma band, not the 125.20 central value.", ) v.check( "central c4b gap after a+c", c4_req_central - (c4a + c4c), 0.015, rel=5e-2, detail="Expected fail: using the true central c4 target, the b-gap is about +0.77, not +0.015.", ) dm_dc4 = (V_EW / 2) * LAM4 / (2 * math.sqrt(radicand)) v.check("dm_H/dc4 magnitude", dm_dc4, 0.149, rel=5e-3) v.check( "c4 tolerance from sigma_H", SIGMA_H / dm_dc4, 0.3, rel=5e-2, detail="Expected fail: the derivative gives a 1-sigma c4 tolerance about 0.74; 0.3 is a stricter heuristic, not the value from +/-0.11 GeV.", ) # Orbit-factor proof checks. v.check( "generic G2 pair orbit dimension from SU(2) stabilizer", 14 - 3, 10, rel=1e-12, detail="Expected fail: the actual orbit dimension is 11 before the paper's extra normalization subtraction.", ) v.check( "topology b c4 using raw orbit dimension 11", (1 / 16) * (4 / 11), 1 / 40, rel=1e-3, detail="Expected fail: without the ad hoc 11->10 subtraction, c4b would be 1/44.", ) v.record( "orbit-dimension theorem does not equate 14-3 with 11-1", "14 - 3 = 11 - 1 = 10" not in TEX, "paper writes 14 - 3 = 11 - 1 = 10", "14 - 3 = 11", "Expected fail: the pure orbit dimension is 11; the additional normalization step is a separate convention and needs proof.", ) v.record( "comparison with P101 has no zero-shift wording", "+0.0071960 - 0.0071960 = 0" not in TEX, "paper says topology b shifts the radicand by +0.0071960 - 0.0071960 = 0", "shift = c4b*lambda^4", "Expected fail: the actual P101->P102 radicand shift is small but nonzero, about 0.000061.", ) sys.exit(v.summary())