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"""v275 -- QGAMB.ROADMAP.01: the obligation roadmap for QG.AMB.01 (the ambient /
metric-sector measure = full nonperturbative quantum gravity), consolidated into one
module.  QG.AMB.01 is the single genuine STRUCTURAL frontier; it has a rich support
chain (Tier A decoupling, Tier B boundary-net reduction) but no module of its own --
this gives it one, and states honestly what is discharged toward it and what stays
open.  It does NOT close QG.AMB.01.

  [E] 1. TIER A -- GAP DECOUPLING (discharged).  the admissible sector keeps a
        strictly positive effective gap under metric dressing,
        Delta_eff = 6 log(3/2) - 31/(4 pi^2) = 1.648 > 0 (v36/v76), with the metric
        perturbation bounded by 2||V|| <= 2 * 248 c3^2 = 31/(4 pi^2) = 0.785.  So
        EVERY testable low-energy readout (masses, mixings, alpha^-1, R+R^2) is
        independent of the un-built ambient measure -- QG.AMB.01 is gap-decoupled,
        NOT a blocker for any SM/cosmology test.
  [E] 2. TIER B -- BOUNDARY-NET REDUCTION (reduced, not closed).  the ambient bulk
        measure reduces to identifying the seam-Calderon boundary measure with the
        holomorphic (E8)_1 conformal net (c = 248/31 = 8 = rank E8; v77, GATE.METRIC.03),
        the gap giving clustering -> tightness of the boundary projective limit.
        Residual = the constructive seam-Calderon -> (E8)_1 map + bulk reconstruction
        (REDTEAM.A.01: "reduced to a boundary-net problem", do NOT write "closed").
  [C] 3. PERTURBATIVE LAYER (in hand, v269/v271/v273).  the 4D perturbative S-matrix
        S_pert is Epstein-Glaser-constructible (v269) with concrete one-loop numbers
        (v271 quartic, v273 gauge (41/10,-19/6,-7)) -- the perturbative 4D content is
        in hand; QG.AMB.01 is specifically the NONPERTURBATIVE ambient measure on top.
  [O] 4. THE OPEN CORE.  the nonperturbative interacting ambient measure (the bulk
        path integral / projective limit) is NOT constructed.  This is the one
        genuine structural frontier -- gap-decoupled (Tier A) and reduced to a
        boundary problem (Tier B), but open.
  [X] 5. PROMOTION / KILL.  QG.AMB.01 closes IFF the seam-Calderon boundary measure
        is identified with (E8)_1 AND the bulk reconstruction is proved (constructive-
        QFT grade).  A proof that the seam net is NOT (E8)_1, or that the gap fails
        (Delta_eff <= 0), kills the reduction.  A sharp obligation, not a knob.

Status: [E] Tier A decoupling + the c=8 boundary-net facts; [C] the perturbative
layer; [O] the nonperturbative ambient measure stays open; [X] the promotion/kill
condition.  A consolidation/roadmap that gives the QG.AMB.01 gate a module -- it does
not close it.  Python-only (numerical gap + exact c=8 facts already mirrored via v77).
"""
import sympy as sp

from tfpt_constants import check, summary, reset, c3


def run():
    reset()
    print("v275  QGAMB.ROADMAP.01: the obligation roadmap for QG.AMB.01 (ambient nonperturbative QG)")

    # 1. Tier A: gap decoupling
    Delta = float(-sp.log(sp.Rational(2, 3) ** 6))            # 6 log(3/2)
    two_V = float(2 * 248 * c3 ** 2)                          # 2||V|| <= 2*dim(E8)*c3^2
    Delta_eff = Delta - two_V
    check("TIER A -- GAP DECOUPLING [E]: Delta_eff = 6 log(3/2) - 2*248 c3^2 = %.4f - "
          "%.4f = %.4f > 0 (v36/v76); the admissible sector keeps a positive gap "
          "under metric dressing, so every low-energy readout (masses, mixings, "
          "alpha^-1, R+R^2) is INDEPENDENT of the un-built ambient measure -- "
          "QG.AMB.01 is gap-decoupled, not a blocker"
          % (Delta, two_V, Delta_eff),
          Delta_eff > 1.6 and two_V < Delta)

    # 2. Tier B: boundary-net reduction (c = 248/31 = 8)
    c_E8 = sp.Rational(248, 31)
    check("TIER B -- BOUNDARY-NET REDUCTION [E]/[P]: the ambient bulk measure reduces "
          "to identifying the seam-Calderon boundary measure with the holomorphic "
          "(E8)_1 net (c = 248/31 = %s = rank E8; v77, GATE.METRIC.03), the gap -> "
          "clustering -> tightness. Residual = the constructive seam-Calderon -> "
          "(E8)_1 map + bulk reconstruction (REDTEAM.A.01: reduced, NOT closed)"
          % c_E8, c_E8 == 8)

    # 3. perturbative layer in hand
    check("PERTURBATIVE LAYER [C]: the 4D perturbative S-matrix S_pert is "
          "Epstein-Glaser-constructible (v269) with concrete one-loop numbers (v271 "
          "quartic, v273 gauge (41/10,-19/6,-7)) -- the perturbative 4D content is in "
          "hand; QG.AMB.01 is specifically the NONPERTURBATIVE ambient measure on top", True)

    # 4. the open core
    check("OPEN CORE [O]: the nonperturbative interacting ambient measure (the bulk "
          "path integral / projective limit) is NOT constructed -- the one genuine "
          "structural frontier, gap-decoupled (Tier A) and reduced to a boundary "
          "problem (Tier B), but open", True)

    # 5. promotion / kill
    check("PROMOTION / KILL [X]: QG.AMB.01 closes IFF the seam-Calderon boundary "
          "measure is identified with (E8)_1 AND the bulk reconstruction is proved "
          "(constructive-QFT grade); a proof that the seam net is NOT (E8)_1, or that "
          "the gap fails (Delta_eff <= 0), kills the reduction -- a sharp obligation", True)

    return summary("v275 QG.AMB.01 roadmap: Tier A decoupled (Delta_eff=1.648>0) + Tier B reduced to (E8)_1 boundary net + perturbative layer in hand; nonperturbative measure stays [O] (QGAMB.ROADMAP.01)")


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

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