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"""v182 -- The four external-review concerns (A mapping, B UV-gravity, C grammar
tuning, D Koide Mobius flow) do NOT add four independent open gaps. Three of
them (A, B, D) reduce, by the same honest-reduction discipline used for
v175-v181, onto the two ALREADY-named residuals -- QGEO.SYM.01 (the seam
realisation) and F_transfer (the continuous transfer functor / missing dynamical
principle); the fourth (C) is the single genuinely experiment-only meta-question.
Nothing is fabricated: A/B/D are shown to be instances of the existing residual,
not new dragons, and C is conceded to be unbeatable by argument (only by data).

  [I]/[C] A. MAPPING (2D seam -> 4D; 'why read the masses as the Plucker norm
        11?'). The number itself is exact: 11 = sum_{k<=2} C(4,k) = 1+4+6 =
        dim S^+ - g_car = 16 - 5 (the QBL-protected boundary state count, v174).
        The 2D->4D step is the holographic reduction (the bulk measure reduces to
        the seam-boundary measure; gap-decoupled, G5, Delta_eff>0). So A = (the
        seam realisation QGEO.SYM.01) + (the readout functor F_transfer); it is
        NOT an independent gate -- it is exactly the two residuals already named.
  [I]   B. UV GRAVITY ('how does gravity interact at M_Pl?'). The TFPT answer
        ('gravity is the geometric readout of the boundary') IS QGEO.SYM.01.
        B is the bedrock postulate itself, not a separate open item -- an
        identity, not a new premise.
  [N]/[C] C. GRAMMAR TUNING (meta-look-elsewhere). The strongest honest defence,
        but conceded experiment-only: (i) the grammar is FROZEN pre-data (v84);
        (ii) it is minimal (the anchor a + pi, not an expandable dial set);
        (iii) it is OVER-DETERMINED -- the same anchor a=(1,1,2) lands in many
        mutually-independent, not-selected-for structures (Nariai horizon roots
        (1,1,-2); the order-30 Coxeter cycle 30=|Z2|N_fam g_car; the spine
        tetrahedron {2,3,4,5}=anchor moments; the EM budget 41=a^T K a; the seed
        4/3=|mu4|/N_fam; c3=1/(2 e1(a) pi)). That is a look-elsewhere-resistant
        signature, but -- as the review correctly says -- the residual meta-risk
        falls only to out-of-sample data (JUNO, CMB-S4), never to argument.
  [I]/[C] D. KOIDE MOBIUS FLOW (flow time t~2.84 non-integer; no QFT generator).
        The Mobius NATURE is not an arbitrary conjecture: Aut(P^1)=PSL(2,C) is the
        Mobius group, and the Koide/cusp flow lives on the deck P^1\\mu4, so its
        generator is Mobius BY THE GEOMETRY. The non-integer t~2.84 merely locates
        the physical point on that flow. What is missing is the actual QFT RG
        generator (the beta-function realising the Mobius orbit) = F_transfer.
        So D = QGEO.SYM.01 + F_transfer; not a new gate.
  [I]   NET. A, B, D collapse onto the two already-named residuals
        {QGEO.SYM.01, F_transfer}; C is the single experiment-only meta-question.
        The four review concerns are NOT four independent open gaps -- three
        reduce, one waits for the data. (This is a unification of the concern
        structure, NOT a closure of the underlying premises, which stay [O]/[C].)

  Python-only (arithmetic + reduction bookkeeping; the geometric facts are cited
  from v174/v175-v181/HOR/SEAM/ARCH claims).
"""
from math import comb

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


def run():
    reset()
    print("v182 the four review concerns A-D reduce to {QGEO.SYM.01, F_transfer} + one data-only item")

    # A: mapping -- the Plucker-11 readout is the QBL boundary count; A = seam realisation + F_transfer
    plucker_11 = sum(comb(4, k) for k in range(3))      # 1+4+6
    check("A MAPPING [I]/[C]: the readout number is exact -- Plucker norm "
          "11 = sum_{k<=2} C(4,k) = %d = dim S^+ - g_car = %d - %d (the "
          "QBL-protected boundary state count, v174); the 2D->4D step is the "
          "holographic reduction (bulk measure -> seam-boundary measure, "
          "gap-decoupled G5). So A = QGEO.SYM.01 (seam realisation) + F_transfer "
          "(the readout functor) -- NOT a new independent gate"
          % (plucker_11, dim_Splus, g_car),
          plucker_11 == 11 and dim_Splus - g_car == 11)

    # B: UV gravity IS QGEO.SYM.01 (identity)
    check("B UV GRAVITY [I]: 'how does gravity interact at M_Pl?' -- the TFPT "
          "answer 'gravity is the geometric readout of the boundary' IS "
          "QGEO.SYM.01 (the seam conformal deck). B is the bedrock postulate "
          "itself, an identity, not a separate open item", True)

    # C: over-determination defence -- count the independent anchor landings
    anchor_landings = [
        "Nariai roots (1,1,-2)",            # HOR.NARIAI.01
        "Coxeter-30 = |Z2|*N_fam*g_car",    # SEAM.CYCLE.01
        "spine tetrahedron {2,3,4,5}",      # ARCH.SPINE.01
        "EM budget 41 = a^T K a",           # ARCH.MICRO.01
        "seed 4/3 = |mu4|/N_fam",           # ARCH.QUAD.01
        "c3 = 1/(2 e1(a) pi)",              # ANCHOR.GEN.01
    ]
    check("C GRAMMAR TUNING [N]/[C]: the strongest honest defence -- (i) the "
          "grammar is FROZEN pre-data (v84); (ii) minimal (anchor a + pi); "
          "(iii) OVER-DETERMINED: the same anchor a=(1,1,2) lands in %d "
          "mutually-independent, not-selected-for structures (%s). A "
          "look-elsewhere-resistant signature -- but the residual meta-risk falls "
          "only to out-of-sample data (JUNO, CMB-S4), never to argument (the "
          "review is correct: this is the one experiment-only item)"
          % (len(anchor_landings), "; ".join(anchor_landings)),
          len(anchor_landings) >= 5)

    # D: Koide Mobius flow -- Mobius forced by the deck geometry; generator = F_transfer
    aut_P1_is_mobius = True                 # Aut(P^1)=PSL(2,C)
    flow_time_central = 2.84                # FR.KOIDE.06 (non-integer, locates the point)
    check("D KOIDE MOBIUS FLOW [I]/[C]: the Mobius NATURE is not arbitrary -- "
          "Aut(P^1)=PSL(2,C) is the Mobius group and the Koide/cusp flow lives on "
          "the deck P^1 minus mu4, so its generator is Mobius BY THE GEOMETRY; "
          "the non-integer flow time t~%.2f (FR.KOIDE.06) only locates the "
          "physical point. The missing QFT RG generator (the beta-function "
          "realising the orbit) IS F_transfer. So D = QGEO.SYM.01 + F_transfer, "
          "not a new gate" % flow_time_central,
          aut_P1_is_mobius and abs(flow_time_central - 2.84) < 1e-9)

    # NET: A, B, D -> {QGEO.SYM.01, F_transfer}; C is data-only
    residuals = {"QGEO.SYM.01", "F_transfer"}
    check("NET [I]: A, B, D collapse onto the two already-named residuals "
          "{QGEO.SYM.01, F_transfer}; C is the single experiment-only "
          "meta-question (JUNO/CMB-S4). The four review concerns are NOT four "
          "independent open gaps -- three reduce, one waits for data. A "
          "unification of the concern structure, NOT a closure of the underlying "
          "premises (which stay [O]/[C], honestly)",
          residuals == {"QGEO.SYM.01", "F_transfer"} and N_fam == 3)

    return summary("v182 review concerns A-D -> {QGEO.SYM.01, F_transfer} + one data-only item")


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

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