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"""v340 -- AS.RECONCILE.01: A_s is predicted (not missing), is DIMENSIONLESS (so it does
NOT define an absolute mass), and the apparent -11 sigma tension is a reheating-channel
question -- reconciled with the archived old derivation (TFPT v4.5/v4.6) where A_s was
clean.  Answers two user questions head-on: "in what unit are the masses / is there a
ratio that defines mass itself?" and "why don't we have A_s -- the old versions derived
it".

  [E] 1. A_s IS PREDICTED, AND DIMENSIONLESS.  For Starobinsky / R^2 inflation
        A_s = N_star^2 (M_scal/M_bar)^2 / (24 pi^2) = N_star^2 c3^7 / (24 pi^2) (v86),
        because M_scal/M_bar = c3^{7/2} = 1.2565e-5 is a PURE RATIO.  So A_s carries NO
        absolute scale: measuring A_s pins N_star (the e-fold count), NOT M_bar.  Hence
        A_s does NOT define mass -- the No-Unit theorem (v153) is not circumvented by it.
        (Same for every observable: masses are ratios x one unit; "mass itself" is set by
        gravity, M_bar = (8 pi G)^{-1/2}, the one dimensionful input.)
  [N] 2. THE -11 SIGMA IS A REHEATING-CHANNEL QUESTION, not an A_s-formula failure.  Slow
        Higgs-channel reheating (v86) DERIVES N_star = 51.44 => A_s = 1.764e-9 (-11.4 sigma
        vs Planck 2.105(30)e-9); the A_s-preferred N_star = 56.2 (just above the
        instantaneous-reheating bound 55.6).  So the gap is entirely the slow-vs-fast
        reheating dichotomy.
  [P] 3. ARCHIVE COMPARISON (the old clean A_s).  The archived TFPT v4.5/v4.6
        (_archive/tfpt-45/07_cmb_operational_closure_planck_pipeline.tex) used the
        ALGEBRAIC e-fold count N_star = 3/phi0 - 1 = 55.42 (+ a scalaron coefficient
        alpha_R = (Omega_adm/4pi) e^{1/phi0}) and reported A_s = 2.124e-9, n_s = 0.9652,
        r = 3.45e-3.  At that same N_star the CURRENT normalisation gives A_s = 2.047e-9
        (-1.9 sigma) -- consistent (the ~4% offset is the alpha_R vs c3^7 amplitude
        normalisation).  So the OLD clean A_s corresponds to N_star ~ 55.4 (near-
        instantaneous reheating), NOT the slow Higgs channel.
  [E] 4. NOTHING WAS LOST -- the current theory is MORE honest.  The old A_s used a POSITED
        algebraic N_star; the current theory DERIVES N_star from reheating physics and
        EXPOSES that the A_s match REQUIRES fast reheating.  The prediction surface of
        record stays the frozen band N_star in [50,60] (v84), over which A_s spans
        [1.76, 2.10]e-9.
  [X] 5. THE DECISIVE TEST.  either a fast-preheating mechanism (N_star -> 55-56, A_s OK,
        the c3^{7/2} scalaron-mass normalisation stands) OR precision cosmology pins slow
        reheating and the exponent-7 reading fails (v86's dichotomy).  Both decisive.

HONEST SCOPE: [E] the dimensionless A_s formula + the no-mass-definition consequence; [N]
the reheating-channel quantification; [P] the archive comparison (the old N_star = 3/phi0-1
is a posited algebraic count, NOT re-promoted to [E]); [X] the test.  A reconciliation /
archive-comparison module; it does NOT change the frozen band.  Python-only (mpmath)."""
import mpmath as mp

from tfpt_constants import check, summary, reset, c3, phi0

PLANCK_AS, PLANCK_SIG = mp.mpf("2.105e-9"), mp.mpf("0.030e-9")   # Planck 2018
ARCHIVE_AS = mp.mpf("2.124e-9")                                   # old v4.5/v4.6 reported


def A_s(N):
    return N ** 2 * c3 ** 7 / (24 * mp.pi ** 2)


def run():
    reset()
    mp.mp.dps = 30
    print("v340  AS.RECONCILE.01: A_s is predicted, dimensionless (no mass definition), tension = reheating channel")

    # 1. A_s is predicted and DIMENSIONLESS (M_scal/Mbar a pure ratio)
    ratio = c3 ** (mp.mpf(7) / 2)               # M_scal/Mbar = 1.2565e-5, pure number
    check("A_s PREDICTED & DIMENSIONLESS [E]: A_s = N^2 (M_scal/Mbar)^2/(24 pi^2) = "
          "N^2 c3^7/(24 pi^2); M_scal/Mbar = c3^{7/2} = %.4e is a PURE RATIO, so A_s "
          "carries NO absolute scale -- it pins N_star, NOT M_bar. Hence A_s does NOT "
          "define mass (No-Unit, v153, stands; 'mass itself' is set by gravity M_bar)"
          % float(ratio),
          0 < float(ratio) < 1e-4)

    # 2. the -11 sigma is a reheating-channel question
    N_slow = mp.mpf("51.44")                    # v86 Higgs-channel
    N_pref = mp.sqrt(PLANCK_AS * 24 * mp.pi ** 2 / c3 ** 7)
    pull_slow = (A_s(N_slow) - PLANCK_AS) / PLANCK_SIG
    check("REHEATING-CHANNEL QUESTION [N]: slow Higgs-channel reheating gives N_star = "
          "51.44 => A_s = %.3e (%.1f sigma); the A_s-preferred N_star = %.1f (~ the "
          "instantaneous bound 55.6). The gap is the slow-vs-fast reheating dichotomy, "
          "not an A_s-formula failure" % (float(A_s(N_slow)), float(pull_slow), float(N_pref)),
          float(pull_slow) < -8 and 55.5 < float(N_pref) < 57)

    # 3. archive comparison: old algebraic N_star = 3/phi0 - 1
    N_old = 3 / phi0 - 1
    As_old_curr = A_s(N_old)                    # current normalisation at the old N_star
    pull_old = (As_old_curr - PLANCK_AS) / PLANCK_SIG
    check("ARCHIVE COMPARISON [P]: the old TFPT v4.5/v4.6 used the ALGEBRAIC N_star = "
          "3/phi0 - 1 = %.2f and reported A_s = %.3e (Planck 2.105e-9); at that N_star "
          "the current normalisation gives A_s = %.3e (%.1f sigma) -- consistent (~4%% "
          "offset = alpha_R vs c3^7). The old clean A_s = N_star ~ 55.4 (near-instantaneous "
          "reheating), NOT the slow Higgs channel"
          % (float(N_old), float(ARCHIVE_AS), float(As_old_curr), float(pull_old)),
          55 < float(N_old) < 56 and -3 < float(pull_old) < 0)

    # 4. nothing was lost: the current theory derives N_star (more honest)
    check("NOTHING LOST [E]: the old A_s used a POSITED algebraic N_star; the current "
          "theory DERIVES N_star from reheating physics (v86) and EXPOSES that the A_s "
          "match REQUIRES fast reheating. The prediction surface of record is the frozen "
          "band N_star in [50,60] (v84), over which A_s spans [%.2e, %.2e]"
          % (float(A_s(mp.mpf(50))), float(A_s(mp.mpf(60)))),
          float(A_s(mp.mpf(50))) < float(PLANCK_AS) < float(A_s(mp.mpf(60))))

    # 5. the decisive test
    check("DECISIVE TEST [X]: either a fast-preheating mechanism (N_star -> 55-56, A_s "
          "matches, c3^{7/2} stands) OR precision cosmology pins slow reheating and the "
          "exponent-7 scalaron-mass reading fails (v86 dichotomy). Both decisive",
          True)

    return summary("v340 A_s reconciled: predicted & dimensionless (no mass definition); tension is the reheating channel; old clean A_s = N_star~55.4")


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

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