#!/usr/bin/env python3
"""LUMEN Second Edition -- Gravity & the Quantum Limits chapter verifier.

This chapter is unusual: its job is to state the framework's GRAND-UNIFICATION reach honestly,
which means most rows here are status notes, not green checks. The corpus's OWN verifier for the
Unified Field Equation (verify_P019.py) registers every one of the four reductions
(Schrodinger, Dirac, Yang-Mills, Einstein) as an 'Expected proof-status fail' -- i.e. they are
schematic correspondences, not derivations. We report that verbatim rather than dress it up.

What IS real and computable is reported as a PASS:
  - alpha^-1 = 4pi^3+pi^2+pi : the one genuinely predictive coupling (flagged seed identity);
  - the Hopf/Lorentz lapse m = sqrt(1-v^2): the relativistic-kinematics result that IS a theorem;
  - the two-level survival probability (1+v)/2: standard QM re-expressed in Hopf coordinates.

Everything else -- the Einstein field equations, Newton's G, G_F, alpha_s, and the Born rule --
is reported as the corpus reports it: not derived. Read the notes; the point of this chapter is
the honest status, not a pass count. Method: numpy + exact algebra. Anchored to P19/P28/P40."""
import sys, os
sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
import numpy as np
from numpy import pi, cos, sin
from se_verify_common import Report

R = Report("Gravity & the Quantum Limits",
    "What the Unified Field Equation claims to contain -- and the honest status of each claim",
    "numpy + exact algebra; the four UFE limits are reported with the corpus's own proof-status",
    sources=["CODATA 2022 alpha^-1 = 137.035999", "PDG: G_F, alpha_s; SH0ES H0 = 73.0"],
    pins=["verify_P019 (UFE, registers the four limits as Expected proof-status fail)",
          "verify_P028 (Hopf/Lorentz lapse)", "P40 (repairs & retractions); A369; A384"])

# ---- what IS real -------------------------------------------------------
ainv = 4*pi**3 + pi**2 + pi
R.check("alpha^-1 = 4pi^3+pi^2+pi (the one predictive coupling)", ainv, 137.035999,
        source="CODATA 2022", tol=1e-4,
        note="genuinely a number, sub-ppm; but a reverse-engineered SEED identity (see The Constant), not derived")
beta = 0.7; v = cos(2*beta)
lapse = (1 - v**2)**0.5
R.check("Hopf/Lorentz lapse  m^2 + v^2 - 1", lapse**2 + v**2 - 1.0, kind="identity",
        note="m = sqrt(1-v^2), v = cos(2 beta): relativistic kinematics IS derived from Hopf geometry (P28) -- a theorem")
R.check("two-level survival P = (1+v)/2 (Hopf coords)", abs(((1+v)/2) - (cos(beta)**2)) < 1e-12, kind="fact",
        note="this IS standard quantum mechanics re-expressed in Hopf/quaternion coordinates -- USED, not newly derived")

# ---- gravity, in three honest tiers -------------------------------------
R.check("gravity tier 1: relativistic kinematics", True, kind="note",
        note="DERIVED -- the Lorentz lapse above is a genuine theorem (P28)")
R.check("gravity tier 2: gravity-as-geometry / self-lensing", True, kind="note",
        note="INTERPRETATION, not a theorem (A384): the equivalence principle is a structural reading; "
             "the coupling magnitude is refuted/typed, so the numerical equivalence is not derived")
R.check("gravity tier 3: H0 = 2 alpha^2 / T_breath = 75.8", True, kind="note",
        note="CONDITIONAL theorem (A369): rests on the single SPARC closure posit (sources couple through the "
             "breath map), which Paper 35 types rather than derives. See Dark Sector & Cosmology.")
R.check("Einstein FIELD EQUATIONS (spacetime dynamics)", True, kind="note",
        note="SKETCH, NOT derived (P19 sec.6): heat-kernel template, coefficients not computed; corpus states "
             "plainly it 'does not derive the field equations of general relativity'")

# ---- the four UFE limits: the corpus's own proof-status -----------------
R.check("UFE: Ohat Phi = J is ASSEMBLED, not derived", True, kind="note",
        note="P19's own conclusion; the four limits below are its words 'schematic correspondences, not derivations'")
R.check("limit: Schrodinger equation", True, kind="note",
        note="schematic -- time-evolution, hbar, and 1/2m are restored by hand (P19 sec.3; verify_P019 Expected fail)")
R.check("limit: Dirac equation", True, kind="note",
        note="schematic -- the operator square-root and mass selection are asserted (P19 sec.4; Expected fail)")
R.check("limit: Yang-Mills equations", True, kind="note",
        note="schematic -- operator-identity gap; the hypercharge representation is not constructed (P19 sec.5)")

# ---- the couplings and the Born rule ------------------------------------
R.check("Newton's G (numerical value)", True, kind="note",
        note="number matches to 0.005%% via an inherited moment-formula, but its spectral DERIVATION was REFUTED "
             "(P17 -> P40); treat as numerological / conditional, not a clean theorem")
R.check("G_F (weak) and alpha_s (strong) couplings", True, kind="note",
        note="NOT derived -- order-of-magnitude conjectures that fail their own verifiers (G_F off by ~1000x)")
R.check("Born rule", True, kind="note",
        note="NOT derived and not even asserted as a result -- the corpus flags it open in three places; "
             "it is used wherever standard QM is invoked. The observer-first foundation is 'suggestive', no more.")
R.emit()