#!/usr/bin/env python3
"""
verify_P019.py -- Paper 19: unified field equation synthesis.

This verifier checks the concrete arithmetic and proof-status claims in
toe/19_Paper_UnifiedFieldEquation.tex. P19 mostly synthesizes P18/P20-style
claims, so the verifier separates reproducible coefficient arithmetic from
claims that the standard Schrodinger, Dirac, Yang-Mills, and Einstein equations
are actually derived from the UFE in this TeX.

The basic constants reproduce: alpha=1/mu0, gamma=3/4, kappa=alpha^(5/4),
beta=3pi/20, the Planck-log formula, beta_geom=mu1/mu0, and the 3/11
dimension-ratio Weinberg estimate. The flagged issues are status/formula
problems: several coupling estimates are heuristic or dimensionally incomplete,
the cosmological-constant scaling does not give 1e-122 by itself, the beta
origin table is inconsistent with the standard B4 volume, and the four field
equation reductions are schematic rather than derived.
"""

from __future__ import annotations

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: inherits Verifier's tolerance logic unchanged,
    emits the corpus's modern check-line format (numbered [PASS]/[FAIL]
    lines, computed/claimed as indented info lines)."""

    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)
        desc = label if (ok or not detail) else f"{label} -- {detail}"
        print(f"  [{'PASS' if ok else 'FAIL'}] {n:>2}. {desc}")
        if computed != "" or claimed != "":
            print(f"        computed: {computed}")
            print(f"        claimed : {claimed}")
        if ok and detail:
            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


v = ModernVerifier("P019 -- Unified Field Equation")

ROOT = Path(__file__).resolve().parents[2]
TEX = (ROOT / "toe" / "19_Paper_UnifiedFieldEquation.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
MU2 = 16.0 * PI**3 / 6.0 + 3.0 * PI**2 / 5.0 + 2.0 * PI / 4.0
ALPHA = 1.0 / MU0
GAMMA = 3.0 / 4.0
KAPPA = ALPHA**1.25
BETA = 3.0 * PI / 20.0
E_SELF = 13.176712697
V4_UNIT_BALL = PI**2 / 2.0

MPL_GEV = 1.22089e19
ME_GEV = 0.00051099895
MW_GEV = 80.379
GF_OBS = 1.1663787e-5
SIN2W_MZ = 0.2312


def pct(value: float, target: float) -> float:
    return 100.0 * (value - target) / abs(target)


planck_log = BETA * MU1 / (1.0 - MU1 * ALPHA**2)
observed_planck_log = math.log(MPL_GEV / ME_GEV)
alpha_weak = 3.0 / (4.0 * MU0)
alpha_strong = 2.0 / MU0
sin2w_dim = 3.0 / (3.0 + 8.0)
gf_formula = ALPHA / (MU1 * MW_GEV**2)
lambda_naive = MU2 / MU0**4
beta_origin_with_standard_v4 = 3.0 * PI / (4.0 * V4_UNIT_BALL)

v.check("mu0 alpha inverse", MU0, 137.036, rel=3e-6)
v.check("mu1", MU1, 108.717, rel=3e-6)
v.check("mu2", MU2, 90.176, rel=5e-7)
v.check("alpha coefficient", ALPHA, 1.0 / 137.036, rel=3e-6)
v.check("gamma coefficient", GAMMA, 0.75, rel=1e-12)
v.check("kappa coefficient", KAPPA, 0.002132826, rel=7e-8)
v.check("beta coefficient", BETA, 0.471239, rel=3e-7)
v.check("self-lensing amplitude E_self/mu0^2", E_SELF / MU0**2, 0.0007016, rel=2e-4)
v.check("Planck log formula", planck_log, 51.53, rel=4e-6)
v.check("Planck log observed comparison", observed_planck_log, 51.5271, rel=2e-5)
v.check("geometric beta mu1/mu0", MU1 / MU0, 0.7933, rel=6e-5)

v.check("alpha_weak dimension ratio formula", alpha_weak, 3.0 / (4.0 * MU0), rel=1e-12)
v.check("alpha_strong dimension ratio formula", alpha_strong, 2.0 / MU0, rel=1e-12)
v.check("weak mixing dimension ratio", sin2w_dim, 3.0 / 11.0, rel=1e-12)
v.check("weak mixing rounded value", sin2w_dim, 0.27, rel=2e-2)
v.record(
    "3/11 weak-mixing estimate is close to measured 0.23",
    abs(pct(sin2w_dim, SIN2W_MZ)) < 5.0,
    computed=f"3/11 = {sin2w_dim:.6f}, gap = {pct(sin2w_dim, SIN2W_MZ):+.2f}%",
    claimed="close to measured value ~0.23",
    detail="Expected precision/wording fail.",
)

v.check(
    "beta origin using standard unit B4 volume",
    beta_origin_with_standard_v4,
    BETA,
    rel=5e-3,
    detail="Expected fail: dim(S3)*pi/(dim(B4)*Vol(B4)) with Vol(B4)=pi^2/2 gives 3/(2pi), not 3pi/20.",
)
v.check(
    "naive cosmological constant scale mu2/mu0^4",
    lambda_naive,
    1e-122,
    rel=1.0,
    detail="Expected fail: the displayed proportionality alone gives about 2.6e-7, not 1e-122.",
)
v.check(
    "Fermi coupling estimate alpha/(mu1 MW^2)",
    gf_formula,
    GF_OBS,
    rel=5e-1,
    detail="Expected fail: direct GeV substitution is about 0.09% of observed G_F.",
)
v.record(
    "strong-coupling estimate supplies running factor",
    False,
    computed=f"mu0/2 = {MU0/2.0:.3f}; reaching alpha_s^-1~8.5 requires an unspecified f(running)~0.124",
    claimed="alpha_s^-1 ~ mu0/2 * f(running) approx 8-9",
    detail="Expected reproducibility fail.",
)

v.record(
    "action variation is complete with field-dependent source",
    False,
    computed="J is defined from a self-interaction functional, but the variation treats J as independent of Phi and drops delta J terms/boundary variations",
    claimed="delta S/d Phi^dagger = O Phi - J",
    detail="Expected variational-proof fail.",
)
v.record(
    "Schrodinger equation is derived rather than restored by hand",
    False,
    computed="the proof starts from an eigenvalue equation, then inserts time dependence, hbar, and 1/(2m) by restoration of units",
    claimed="UFE reduces to the Schrodinger equation",
    detail="Expected proof-status fail.",
)
v.record(
    "Dirac equation follows from a justified square root of the UFE",
    False,
    computed="taking a square root of D_B4^2 and selecting m_n is asserted; no spectral factorization or boundary-domain argument is supplied",
    claimed="UFE reduces to the Dirac equation",
    detail="Expected proof-status fail.",
)
v.record(
    "Yang-Mills equation follows from Delta_S3 A = D_mu F^mu nu",
    False,
    computed="the connection Laplacian on S3 is not generally equal to the nonlinear Yang-Mills operator without gauge fixing and curvature terms",
    claimed="Delta_S3 acting on gauge fields gives D_mu F^mu nu",
    detail="Expected operator-identity fail.",
)
v.record(
    "division-algebra gauge-group derivation is exact here",
    False,
    computed="the R,C,H,O to U(1),SU(2),SU(3) dictionary inherits P37 caveats and does not construct the SM hypercharge representation",
    claimed="SM gauge group determined by division algebras",
    detail="Expected status fail.",
)
v.record(
    "Einstein equations are derived with computed heat-kernel coefficients",
    False,
    computed="a heat-kernel template is written, but a2, Lambda, the cutoff, and the stress tensor are not computed from the UFE",
    claimed="coarse-graining the UFE yields Einstein field equations",
    detail="Expected proof-status fail.",
)
v.record(
    "all coupling constants are encoded and derived from rho moments in P19",
    False,
    computed="alpha and the inherited Planck-log formula are numeric; alpha_s, G_F, weak mixing, and Lambda are heuristic/open in this TeX",
    claimed="all coupling constants derive from rho(x) moments",
    detail="Expected status fail.",
)
v.record(
    "prediction list is derived in this paper",
    False,
    computed="no fourth family, CP phase, strong CP, and proton-stability statements are asserted without the needed topology/anomaly/operator proofs",
    claimed="UFE predicts no fourth family, CP phase, strong CP, proton stability",
    detail="Expected proof-status fail.",
)
v.record(
    "zero-free-parameter all-physics conclusion is supported",
    False,
    computed="several reductions and coupling estimates are schematic or inherited from papers with open caveats",
    claimed="One equation. Zero parameters. All physics.",
    detail="Expected status fail.",
)
v.record(
    "cosmological constant derivation is explicitly open",
    "detailed derivation remains an open problem" in TEX,
    computed="open-problem caveat present",
    claimed="Lambda derivation not closed",
)

sys.exit(v.summary())