#!/usr/bin/env python3 """ verify_P119.py -- Addendum 119: rho EM self-energy. This verifier checks the rho^0 VMD correction arithmetic in 119_Addendum_RhoEMSelfEnergy.tex: the J1 bare 8*pi coupling, monadic integral pi, delta_rho = pi*alpha, corrected f_rho^2, charge-factor suppression, omega/phi table values, and the correction hierarchy. The main rho correction is numerically reproducible. Flagged issues are sign/rounding/status problems: the exact TOE-minus-PDG rho residual is negative, the exact gap-closed fraction slightly overshoots 100% rather than giving 99.6%, the abstract/body residual sign conventions conflict, and the "complete sector" wording is stronger than the paper's own open items about omega/phi residuals and monadic-term selection. """ from __future__ import annotations import math import sys from pathlib import Path PASS = FAIL = 0 _N = 0 def record(label, ok, computed="", claimed="", detail=""): """Modern-format check line; behavior-preserving port of verify_common.""" global PASS, FAIL, _N _N += 1 ok = bool(ok) desc = label if ok: PASS += 1 else: FAIL += 1 if "Expected" in detail: i = detail.find("Expected") desc = f"{label} -- {detail[i:]}" detail = detail[:i].rstrip().rstrip(";") print(f" [{'PASS' if ok else 'FAIL'}] {_N:>2}. {desc}") if computed != "" or claimed != "": print(f" computed: {computed}") print(f" claimed : {claimed}") if detail: print(f" {detail}") return ok def check(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 record(label, ok, computed, claimed, err_detail + (f"; {detail}" if detail else "")) print("P119 -- rho EM Self-Energy") ROOT = Path(__file__).resolve().parents[1] TEX = (ROOT / "119_Addendum_RhoEMSelfEnergy.tex").read_text() PI = math.pi MU0 = 4.0 * PI**3 + PI**2 + PI MU1 = 16.0 * PI**3 / 5.0 + 3.0 * PI**2 / 4.0 + 2.0 * PI / 3.0 MU = MU1 / MU0 ALPHA = 1.0 / MU0 ALPHA_S = 0.1186 PDG_RHO = 24.56 PDG_OMEGA = 290.97 PDG_PHI = 179.1 C_RHO2 = 1.0 / 2.0 C_OMEGA2 = 1.0 / 18.0 C_PHI2 = 1.0 / 9.0 J1_BARE = 8.0 * PI MONADIC_INTEGRAL = PI DELTA_RHO = PI * ALPHA F_RHO = J1_BARE * (1.0 - DELTA_RHO) RHO_ORIGINAL_GAP = 100.0 * (J1_BARE - PDG_RHO) / J1_BARE RHO_RESIDUAL = 100.0 * (F_RHO - PDG_RHO) / PDG_RHO GAP_CLOSED = 100.0 * (J1_BARE - F_RHO) / (J1_BARE - PDG_RHO) F_OMEGA = 72.0 * PI / (1.0 - ALPHA_S) ** 2 F_PHI = 36.0 * PI / MU**2 OMEGA_RESIDUAL = 100.0 * (F_OMEGA - PDG_OMEGA) / PDG_OMEGA PHI_RESIDUAL = 100.0 * (F_PHI - PDG_PHI) / PDG_PHI OMEGA_EM = DELTA_RHO / 9.0 F_OMEGA_WITH_EM = F_OMEGA * (1.0 - OMEGA_EM) OMEGA_WITH_EM_RESIDUAL = 100.0 * (F_OMEGA_WITH_EM - PDG_OMEGA) / PDG_OMEGA PEIRCE_GEOM_CORRECTION = 1.0 / MU**2 - 1.0 def pct(value: float, target: float) -> float: return 100.0 * (value - target) / abs(target) check("alpha inverse mu0", MU0, 137.036, rel=3e-6) check("bare J1 f_rho^2 = 8*pi", J1_BARE, 25.133, rel=2e-5) check("P108 original gap magnitude percent", RHO_ORIGINAL_GAP, 2.28, rel=5e-3) record( "P108 bare value overshoots PDG rho", J1_BARE > PDG_RHO, computed=f"bare={J1_BARE:.6f}, PDG={PDG_RHO:.2f}", claimed="bare overshoots by 2.28%", ) check("monadic spectral integral", MONADIC_INTEGRAL, PI, rel=1e-12) check("delta_rho = pi*alpha", DELTA_RHO, 0.022917, rel=5e-4) check("1 - pi*alpha", 1.0 - DELTA_RHO, 0.977083, rel=1e-5) check("corrected f_rho^2", F_RHO, 24.557, rel=2e-5) check( "rho residual sign and value percent", RHO_RESIDUAL, 0.01, rel=1e-1, detail="Expected fail: exact TOE-minus-PDG convention gives about -0.014%, not +0.01%.", ) check( "gap closed percent", GAP_CLOSED, 99.6, rel=2e-3, detail="Expected fail: exact values slightly overclose the gap, giving about 100.6%.", ) check("rho charge factor squared", C_RHO2, 1.0 / 2.0, rel=1e-12) check("omega charge factor squared", C_OMEGA2, 1.0 / 18.0, rel=1e-12) check("phi charge factor squared", C_PHI2, 1.0 / 9.0, rel=1e-12) check("omega-to-rho EM suppression", C_OMEGA2 / C_RHO2, 1.0 / 9.0, rel=1e-12) check("omega EM self-energy percent", 100.0 * OMEGA_EM, 0.25, rel=3e-2) check("omega f_V^2 table value", F_OMEGA, 291.2, rel=2e-4) check("omega residual percent", OMEGA_RESIDUAL, 0.08, abs_tol=0.025) check("phi f_V^2 table value", F_PHI, 179.7, rel=7e-4) check("phi residual percent", PHI_RESIDUAL, 0.36, rel=1e-1) check("Peirce geometry correction 1/MU^2 - 1", PEIRCE_GEOM_CORRECTION, 0.589, rel=4e-4) record( "correction hierarchy", DELTA_RHO < ALPHA_S / 3.0 < PEIRCE_GEOM_CORRECTION, computed=f"{DELTA_RHO:.6f} < {ALPHA_S/3.0:.6f} < {PEIRCE_GEOM_CORRECTION:.6f}", claimed="pi alpha < alpha_s/3 < 1/MU^2 - 1", ) check("omega residual after adding suppressed EM percent", OMEGA_WITH_EM_RESIDUAL, -0.19, rel=8e-2) record( "abstract and body use consistent original residual sign", False, computed="abstract says -2.28% discrepancy; setup formula computes +2.28% bare-minus-exp", claimed="one consistent P108 rho residual sign convention", detail="Expected sign-convention fail.", ) record( "neutral vector f_V^2 sector is fully closed at this level", False, computed="open items state omega/phi residuals are not closed at this level and omega EM needs a more careful isoscalar treatment", claimed="This completes the neutral vector meson f_V^2 sector", detail="Expected status fail.", ) record( "monadic-term selection is derived from J3(O) propagator formalism", False, computed="the open-items section says this is argued physically but has not been derived from the propagator formalism", claimed="self-energy uniquely picks the monadic term", detail="Expected proof-status fail.", ) record( "open-items caveats are present in TeX", "not closed at this level" in TEX and "has not been" in TEX, computed="explicit caveats found", claimed="paper records residual and propagator-selection caveats", ) print(f"\n{'='*60}\nRESULT: {PASS} PASS / {FAIL} FAIL") sys.exit(0 if FAIL == 0 else 1)