#!/usr/bin/env python3 """ verify_P080.py -- Addendum 80: MU from the spectral mean of rho. This verifier checks the rho-moment arithmetic and the claimed closure of the P77 spectral-angle assumption. The moment identity itself is correct: MU=mu1/mu0=CGF'(0) is the rho-weighted mean of x. The flagged issues are the stale printed MU value and proof/status jumps: the Hopf derivative calculation does not equal the rho mean, the mass-coordinate conversion direction is reversed in one sentence, and the paper's unconditional Phase-5b closure rests on that unproved angular-conversion identification. """ from __future__ import annotations import math import sys from pathlib import Path import mpmath as mp sys.path.insert(0, str(Path(__file__).resolve().parent)) from verify_common import CheckResult, Verifier class ModernVerifier(Verifier): """Output adapter: modern check-line format. Tolerance logic is inherited unchanged from verify_common.Verifier; only printing and the footer differ.""" def __init__(self, name: str): self.name = name self.results = [] print(name) def record(self, label, ok, computed="", claimed="", detail=""): self.results.append(CheckResult(label, ok, computed, claimed, detail)) n = len(self.results) expected = (not ok) and ("Expected" in str(detail)) desc = f"{label} -- {detail}" if expected else label print(f" [{'PASS' if ok else 'FAIL'}] {n:>2}. {desc}") if computed != "" or claimed != "": print(f" computed: {computed}") print(f" claimed : {claimed}") if detail and not expected: print(f" {detail}") return ok def summary(self): passed = sum(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 mp.mp.dps = 60 v = ModernVerifier("P080 -- MU as Spectral Mean of rho") ROOT = Path(__file__).resolve().parents[1] TEX = (ROOT / "80_Addendum_MUFromDensity.tex").read_text() PI = mp.pi MU0 = 4 * PI**3 + PI**2 + PI MU1 = 16 * PI**3 / 5 + 3 * PI**2 / 4 + 2 * PI / 3 MU = MU1 / MU0 EPS = MU * PI / 6 EPL = mp.mpf("68.096") ER_PRED = EPL - 12 + EPS ER_OBS = mp.mpf("56.502") ER_SIGMA = mp.mpf("0.009") EV = mp.mpf("19.63556749202108") ME_EV = mp.mpf("511000") def f(x: mp.mpf) -> float: return float(x) def rho(x: mp.mpf) -> mp.mpf: return 2 * PI * x + 3 * PI**2 * x**2 + 16 * PI**3 * x**3 v.check("mu0 exact integral", f(MU0), 137.036, rel=3e-6) v.check("mu1 exact integral", f(MU1), 108.717, rel=5e-6) v.check("mu1 edge component", f(2 * PI / 3), 2.0944, rel=2e-5) v.check("mu1 boundary component", f(3 * PI**2 / 4), 7.4022, rel=2e-5) v.check("mu1 bulk component", f(16 * PI**3 / 5), 99.220, rel=5e-5) v.check( "printed MU numeric", f(MU), 0.793338, rel=1e-6, detail="Expected fail: exact mu1/mu0≈0.793342208, so 0.793338 is stale at six decimals.", ) v.check("MU rounded corpus value", f(MU), 0.79334, rel=5e-6) v.check("MU reduced formula", f((192 * PI**2 + 45 * PI + 40) / (240 * PI**2 + 60 * PI + 60)), f(MU), rel=1e-12) v.check("CGF'(0)=mu1/mu0", f(MU1 / MU0), f(MU), rel=1e-12) v.check("spectral mean lies below bulk 4/5", f(MU), 0.8, rel=9e-3) v.check("sector ratio EB/mu0", f((4 * PI**3) / MU0), 0.9051, rel=7e-5) v.check("sector ratio (Eb+EB)/mu0", f((PI**2 + 4 * PI**3) / MU0), 0.9771, rel=3e-5) v.check("alpha-minus-one ratio", f((MU0 - 1) / MU0), 0.9927, rel=5e-5) v.check("boundary EW ratio", f(PI**2 / (PI + PI**2)), 0.7585, rel=7e-5) v.check("mu1 sector decomposition", f((mp.mpf(2) / 3) * PI + (mp.mpf(3) / 4) * PI**2 + (mp.mpf(4) / 5) * 4 * PI**3), f(MU1), rel=1e-12) v.check("epsilon MU*pi/6", f(EPS), 0.415392, rel=5e-6) v.check("E_Pl - E_R predicted gap", f(12 - EPS), 11.584608, rel=5e-6) v.check("E_R predicted", f(ER_PRED), 56.511, rel=8e-6) v.check("E_R sigma with displayed uncertainty", f(abs(ER_PRED - ER_OBS) / ER_SIGMA), 1.02, rel=3e-2) v.record( "mass-coordinate conversion sentence uses the right direction", False, computed="from E=pi+ln(m/me)/MU, dE/dln(m/me)=1/MU", claimed="MU is the conversion factor from log-mass to spectral units", detail="Expected audit fail: the written derivative gives 1/MU for log-mass -> E; MU is the inverse conversion.", ) avg_abs_derivative = mp.quad(lambda x: 2 * mp.sqrt(x * (1 - x)) * rho(x), [0, 1]) / MU0 derivative_at_mean = 2 * mp.sqrt(MU * (1 - MU)) v.check( "Hopf average |dx/dbeta| equals MU", f(avg_abs_derivative), f(MU), rel=5e-3, detail="Expected fail: averaging the actual |d cos^2(beta)/dbeta| gives about 0.693, not MU.", ) v.check( "Hopf derivative at mean x equals MU", f(derivative_at_mean), f(MU), rel=5e-3, detail="Expected fail: evaluating the derivative magnitude at x=MU gives about 0.810, not MU.", ) v.record( "Assumption 4.1 follows from the moment computation alone", False, computed="moment computation proves MU=_rho", claimed="one radian of G2 Cartan angle corresponds to MU spectral units", detail="Expected proof-audit fail: the angular-conversion map is identified with the mean, but not derived from the Hopf/G2 maps.", ) v.record( "Phase 5b is closed without residual assumptions", False, computed="closure depends on the unproved angular-conversion identification above", claimed="Phase 5b closed without qualification", detail="Expected status fail: the rho mean is proved, but the conversion-factor theorem is not established by the displayed calculation.", ) enu = 2 * EV - ER_PRED mnu_mev = ME_EV * mp.e ** (MU * (enu - PI)) * 1000 v.check("neutrino energy from exact rounded inputs", f(enu), -17.239, rel=1e-4) v.check( "predicted neutrino mass", f(mnu_mev), 48.7, rel=2e-3, detail="Expected fail: exact use of the displayed inputs gives about 48.53 meV.", ) v.check( "neutrino sigma vs 49.5±0.35 meV", f(abs(mp.mpf("49.5") - mnu_mev) / mp.mpf("0.35")), 2.3, rel=8e-2, detail="Expected fail: 49.5±0.35 against 48.53 meV is about 2.8 sigma.", ) v.record( "neutrino prediction uses no oscillation input", "No oscillation data enters" in TEX, computed="explicit no-oscillation-data claim present", claimed="status wording recorded", ) sys.exit(v.summary())