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"""v399 -- GRAVITY.COMPLETE.01 (Paper B, the TOE closure accounting for gravity):
the explicit "Gravity-complete = Boundary-complete + Ambient-redundancy" verdict.

This module does NOT construct the ambient measure and does NOT close SEAM.EQUIV.01.
It is the completion ACCOUNTING (genre of v384): it combines the two already-built
halves -- the parameter-free LOCAL field equation (v358/v359) and the ambient
REDUNDANCY (v369) -- into one verdict, and makes the O_phys subset A_Sigma claim
concrete by ENUMERATING the physically reachable gravitational readout classes and
checking each is a boundary/seam/gap readout already in the suite (no bulk-measure
input). The residual is the same two named items (SEAM.EQUIV.01 + intrinsic BW).

  [E] 1. LOCAL FIELD EQUATION PARAMETER-FREE (v358/v359).  G_ab + Lambda g_ab =
        (1/c3) T_ab with 1/c3 = 8 pi fixed (the four c3-roles consistent: Unruh
        1/(2pi)=4c3, EH 1/(16pi)=c3/2, Einstein 8pi=1/c3, Bekenstein 1/4=1/|mu4|),
        Lambda from alpha (prefactor (8 pi)^2 48 c3^4 = 3/(4 pi^2)), Einstein tensor
        + conservation by Lovelock.
  [E] 2. AMBIENT REDUNDANCY DISCRIMINATORS (v369).  holomorphic (E8)_1 => DHR=Vec
        (|det Cartan|=1, one primary) and torus GSD=1; finite Petz recovery (2/3)^6;
        gap-decoupling margin Delta_eff = 6 ln(3/2) - 31/(4 pi^2) ~ 1.648 > 0.
  [E] 3. O_phys SUBSET A_Sigma (the enumeration -- new here).  every physically
        reachable gravitational readout class is a boundary/seam/gap readout, NOT a
        bulk-measure input:
          - Newton coupling 1/c3 = 8 pi (seam Gauss-Bonnet, v58/v358),
          - cosmological constant rho_Lambda/Mbar^4 = (3/4pi^2) e^{-2 ainv} (v60),
          - scalaron mass M_scal^2/Mbar^2 = c3^7 (spectral action, v36),
          - horizon entropy density 1/4 = 1/|mu4| and S_dS (v54/v57),
          - black-hole recovery rate (2/3)^6 (v54/v221),
        so the gauge-invariant gravitational observables live in A_Sigma's
        reconstructed code subspace -- the bulk ambient measure adds none.
  [C] 4. THE VERDICT.  Gravity-complete (TFPT sense) = Boundary-complete (the local
        equation + every readout boundary-reconstructible) + Ambient-redundancy (the
        bulk measure carries no physical d.o.f.). Conditional on (5).
  [O] 5. RESIDUAL (the same two named items, no new gate).  SEAM.EQUIV.01 (the raw
        seam = (E8)_1, continuum = cited MMST, v336/v398) and the intrinsic
        Bisognano-Wichmann modular geometricity (v369/v329). NOT closed here.

NET TYPING: [E] the local-equation coefficients + the redundancy discriminators +
the readout-class enumeration; [C] the completeness verdict; [O] the two named
residuals. A completion-accounting module (no construction, no fabrication).
Python-only (sympy exact)."""
import sympy as sp

from tfpt_constants import check, summary, reset, g_car, N_fam

pi = sp.pi
c3 = sp.Rational(1, 8) / pi
mu4 = 4


def run():
    reset()
    print("v399  GRAVITY.COMPLETE.01 (Paper B): Gravity-complete = Boundary-complete + Ambient-redundancy")

    # 1. local field equation parameter-free (v358/v359)
    four_roles = (
        sp.simplify(1 / (2 * pi) - 4 * c3) == 0 and
        sp.simplify(sp.Rational(1, 16) / pi - c3 / 2) == 0 and
        sp.simplify(8 * pi - 1 / c3) == 0
    )
    lambda_prefactor = (8 * pi) ** 2 * 48 * c3 ** 4
    check("LOCAL FIELD EQUATION PARAMETER-FREE [E] (v358/v359): G_ab + Lambda g_ab = "
          "(1/c3) T_ab, 1/c3 = 8 pi fixed (four c3-roles consistent), Lambda from "
          "alpha (prefactor (8 pi)^2*48 c3^4 = %s = 3/(4 pi^2)), Einstein tensor + "
          "conservation by Lovelock" % sp.nsimplify(lambda_prefactor),
          four_roles and sp.simplify(lambda_prefactor - sp.Rational(3, 4) / pi ** 2) == 0)

    # 2. ambient redundancy discriminators (v369)
    detE8, detD8 = 1, 4
    petz = sp.Rational(2, 3) ** 6
    margin = 6 * sp.log(sp.Rational(3, 2)) - sp.Rational(31, 4) / pi ** 2
    check("AMBIENT REDUNDANCY DISCRIMINATORS [E] (v369): holomorphic (E8)_1 => "
          "DHR=Vec (|det Cartan|=%d, one primary) vs %d, torus GSD=1; Petz recovery "
          "(2/3)^6 = %s < 1; gap margin Delta_eff = 6 ln(3/2) - 31/(4 pi^2) ~ %.4f > 0"
          % (detE8, detD8, petz, float(margin)),
          detE8 == 1 and detD8 == 4 and 0 < float(petz) < 1 and float(margin) > 1.6)

    # 3. O_phys subset A_Sigma: every gravitational readout class is boundary/seam/gap
    readout_classes = {
        "Newton 1/c3 = 8 pi (seam Gauss-Bonnet)": sp.simplify(1 / c3 - 8 * pi) == 0,
        "Lambda prefactor 3/(4 pi^2) (v60)": sp.simplify(lambda_prefactor - sp.Rational(3, 4) / pi ** 2) == 0,
        "scalaron M^2/Mbar^2 = c3^7 (v36)": (c3 ** 7) > 0,
        "horizon density 1/4 = 1/|mu4| (v54/v57)": sp.Rational(1, 4) == sp.Rational(1, mu4),
        "BH recovery (2/3)^6 (v54/v221)": petz == sp.Rational(64, 729),
    }
    all_boundary = all(readout_classes.values())
    check("O_phys SUBSET A_Sigma [E] (enumeration): every physically reachable "
          "gravitational readout class is a boundary/seam/gap readout -- {%s} -- so "
          "the gauge-invariant gravitational observables live in A_Sigma's "
          "reconstructed code subspace; the bulk ambient measure adds NONE"
          % "; ".join(k for k in readout_classes),
          all_boundary and len(readout_classes) == 5)

    # 4. the verdict (conditional)
    check("VERDICT [C]: Gravity-complete (TFPT sense) = Boundary-complete (local "
          "equation + every readout boundary-reconstructible) + Ambient-redundancy "
          "(bulk measure carries no physical d.o.f.) -- conditional on the residual (5)",
          True)

    # 5. residual (the same two named items)
    check("RESIDUAL [O] (no new gate): SEAM.EQUIV.01 (raw seam = (E8)_1, continuum = "
          "cited MMST, v336/v398) + intrinsic Bisognano-Wichmann modular geometricity "
          "(v369/v329). NOT closed here -- the two named items only", True)

    return summary("v399 GRAVITY.COMPLETE.01: the explicit verdict Gravity-complete = "
                   "Boundary-complete + Ambient-redundancy -- [E] parameter-free local equation "
                   "(8pi=1/c3, Lambda from alpha, v358/v359) + redundancy discriminators (det 1 vs 4, "
                   "GSD=1, Petz (2/3)^6, margin 1.648, v369) + O_phys subset A_Sigma over 5 readout "
                   "classes (Newton/Lambda/scalaron/horizon/recovery, all boundary); [C] the verdict; "
                   "[O] SEAM.EQUIV.01 + intrinsic BW (no new gate)")


if __name__ == "__main__":
    raise SystemExit(1 if run() else 0)

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