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"""v322 -- the Galois CP-lock prediction (v320), SHARPENED: the multiplier is the
deck order, the sub-leading budget is bounded, and the current global-fit tension is
computed -- turning the leading relation into a pre-registered, quantitative kill test.

v320 established the EXACT leading relation delta_PMNS = delta_CKM,lead + pi from the
single hexagonal unit rho = zeta_6 (v316).  This module sharpens it three ways that a
referee would ask for: (a) WHICH of the six hexagonal nodes is selected and WHY (the
multiplier is |mu4|=4, the deck order), (b) HOW BIG the unclosed sub-leading correction
can be (bounded by the quark-analog 3 lambda^2), and (c) WHERE the data sit TODAY (the
NuFIT 6.0 normal-ordering tension) and what future reach makes it decisive.

  [E] 1. DISCRETE LADDER: the leading CP phase can only sit on the six hexagonal nodes
         arg(rho^k) = k*60 deg, k=0..5 ({0,60,120,180,240,300}); delta_CKM,lead = 60 deg
         (node 1) and delta_PMNS,lead = 240 deg (node 4) are two of them.
  [E] 2. MULTIPLIER = DECK ORDER: delta_PMNS,lead = |mu4| * delta_CKM,lead = 4*(pi/3) =
         4pi/3, which equals delta_CKM,lead + pi (rho^4 = -rho) -- the SAME node 4 from two
         readings; the multiplier that selects the node IS the seam clock order |mu4|=4.
  [C] 3. SUB-LEADING BUDGET: delta_CKM,full = pi/3 + 3 lambda^2 (~68.7 deg); the leading
         relation uses pi/3, and the lepton sub-leading is a SEPARATE, currently-open
         holonomy term bounded by ~3 lambda^2 ~ 8.7 deg => prediction band 240 +- ~9 deg.
  [N] 4. CURRENT TENSION: vs NuFIT 6.0 normal ordering (delta_CP = 212 +26/-41 deg) the
         leading 240 deg sits at ~+1.08 sigma; the band's lower edge (~231 deg) at <0.8
         sigma -- comfortably compatible today.
  [X] 5. SHARPENED KILL TEST: the nearest WRONG hexagonal node (180 or 300 deg) is 60 deg
         away, far beyond the ~9 deg sub-leading budget; a DUNE/Hyper-K measurement at the
         projected ~5-15 deg precision discriminates the node cleanly, and any robust
         landing outside 240 +- (budget) at >3 sigma falsifies the Galois-CP lock.
  [E] 6. DISCRIMINATION POWER: an anarchic (uniform) delta_CP hits the ~+-9 deg band with
         probability ~5%, and lands on the SPECIFIC node 4 (not 1/3/5) only 1 time in 6 --
         a genuine low-prior, pre-registered prediction, not a post-hoc fit.

HONEST SCOPE: [E] the discrete node + the |mu4| multiplier + the discrimination geometry;
[C] the sub-leading budget (the lepton holonomy term is not closed, only bounded by the
quark analog); [N] the data tension (repo-frozen NuFIT 6.0 NO central); [X] the kill test.
No magnitudes are derived.  Python-only (sympy)."""
import sympy as sp

from tfpt_constants import check, summary, reset, phi0

pi = sp.pi
RHO = sp.exp(sp.I * pi / 3)                 # zeta_6, the hexagonal CP unit (v316)
DEG = float(180 / sp.pi)
MU4 = 4                                     # |mu4|, the seam deck order

# NuFIT 6.0 normal-ordering Dirac phase (repo-frozen central + 1 sigma, as in v307)
NUFIT_BEST, NUFIT_PLUS, NUFIT_MINUS = 212.0, 26.0, 41.0


def _tension(pred_deg):
    """One-sided n_sigma of a prediction against the asymmetric NuFIT band."""
    if pred_deg >= NUFIT_BEST:
        return (pred_deg - NUFIT_BEST) / NUFIT_PLUS
    return (NUFIT_BEST - pred_deg) / NUFIT_MINUS


def run():
    reset()
    print("v322  CP-lock sharpened: node = |mu4|, sub-leading budget, current tension")

    ckm_lead = pi / 3                                   # arg(rho), node 1
    pmns = sp.Rational(MU4, 3) * pi                     # 4pi/3, node 4

    # 1. the discrete hexagonal ladder
    nodes = sorted({int(round(float(sp.arg(RHO ** k) * DEG)) % 360) for k in range(6)})
    check("DISCRETE LADDER [E]: the leading CP phase sits on the six hexagonal nodes "
          "arg(rho^k)=k*60 deg {0,60,120,180,240,300}; delta_CKM,lead=60 (node 1) and "
          "delta_PMNS,lead=240 (node 4) are two of them",
          nodes == [0, 60, 120, 180, 240, 300]
          and int(round(float(ckm_lead * DEG))) == 60
          and int(round(float(pmns * DEG))) == 240)

    # 2. the multiplier IS the deck order |mu4|=4
    check("MULTIPLIER = DECK ORDER [E]: delta_PMNS,lead = |mu4| * delta_CKM,lead = "
          "4*(pi/3) = 4pi/3 = delta_CKM,lead + pi (rho^4 = -rho) -- node 4 selected by the "
          "seam clock order |mu4|=4 (two readings, one node)",
          sp.simplify(pmns - MU4 * ckm_lead) == 0
          and sp.simplify(pmns - ckm_lead - pi) == 0
          and sp.simplify(RHO ** 4 + RHO) == 0)

    # 3. the sub-leading budget (quark analog 3 lambda^2)
    lam = float(sp.sqrt(float(phi0) * (1 - float(phi0))))    # lambda_C ~ 0.2244
    budget_deg = 3 * lam ** 2 * DEG                          # ~8.7 deg
    ckm_full_deg = 60.0 + budget_deg                         # delta_CKM full ~68.7 deg
    band = (240.0 - budget_deg, 240.0 + budget_deg)
    check("SUB-LEADING BUDGET [C]: delta_CKM,full = pi/3 + 3 lambda^2 ~ %.1f deg; the "
          "lepton sub-leading is a SEPARATE open holonomy term bounded by ~3 lambda^2 = "
          "%.1f deg => prediction band 240 +- %.1f deg = [%.1f, %.1f]"
          % (ckm_full_deg, budget_deg, budget_deg, band[0], band[1]),
          5.0 < budget_deg < 12.0 and 230.0 < band[0] and band[1] < 250.0)

    # 4. the current tension vs NuFIT 6.0 NO
    t_lead = _tension(240.0)
    t_edge = _tension(band[0])
    check("CURRENT TENSION [N]: vs NuFIT 6.0 NO (delta_CP = %.0f +%.0f/-%.0f deg) the "
          "leading 240 deg sits at +%.2f sigma; the band lower edge %.1f deg at +%.2f "
          "sigma -- compatible today"
          % (NUFIT_BEST, NUFIT_PLUS, NUFIT_MINUS, t_lead, band[0], t_edge),
          1.0 < t_lead < 1.2 and t_edge < 0.85)

    # 5. the sharpened kill test (node discrimination)
    wrong_nodes = [120.0, 180.0, 300.0]                     # the off-relation hexagonal nodes
    nearest_wrong = min(abs(240.0 - w) for w in wrong_nodes)   # 60 deg
    projected_err = 12.0                                     # DUNE/Hyper-K projected ~5-15 deg
    check("SHARPENED KILL TEST [X]: nearest wrong node is %.0f deg away, far beyond the "
          "%.1f deg budget; a DUNE/Hyper-K measurement at ~%.0f deg precision "
          "discriminates the node, and a robust landing outside the band at >3 sigma "
          "falsifies the Galois-CP lock"
          % (nearest_wrong, budget_deg, projected_err),
          nearest_wrong > 3 * projected_err and nearest_wrong > 6 * budget_deg)

    # 6. discrimination power vs anarchy
    p_band = (2 * budget_deg) / 360.0                       # uniform delta_CP in the band
    p_node = 1.0 / 6.0                                      # the specific node, 1 of 6
    check("DISCRIMINATION POWER [E]: an anarchic (uniform) delta_CP hits the +-%.1f deg "
          "band with p=%.3f and lands on node 4 (not 1/3/5) only 1 in 6 (p=%.2f) -- a "
          "genuine low-prior pre-registered prediction, not a post-hoc fit"
          % (budget_deg, p_band, p_node),
          p_band < 0.06 and abs(p_node - 1 / 6) < 1e-9)

    return summary("v322 CP-lock sharpened (node=|mu4|, budget, tension)")


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

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