"""v18 -- A4: the full charged-fermion Yukawa sector and quark c-readout.

Builds on v17 (the finite resolvent backbone).  Using the theorem-output transport
amplitudes Lambda_{f,j} (Paper-3 table "yukawa-residuals", derived from the
hexagonal resolvent at the closed pole delta_ph) and the word-lengths L_{f,j}, the
intrinsic Yukawas are

    y_{f,j} = lambda_Y^{L_{f,j}} * Lambda_{f,j},   lambda_Y = sqrt(phi0 (1-phi0)).

This script:
  (1) reproduces the theory's quoted closed-branch quark SOURCE RATIOS
      (mu/md = 0.470085, mc/ms = 13.61, mt/mb = 40.80) to 4-5 digits;
  (2) reproduces the lepton c-form  lambda_Y^L Lambda = pi c phi0^n  with
      c = (16/7, 4/3, 7/6) at n = (5,3,2), to the 3-digit Lambda rounding;
  (3) checks the full 9-fermion hierarchy ordering;
  (4) shows the source ratios match observed (PDG) ratios where the comparison is
      scheme-light (mu/md, mc/ms, m_mu/m_tau, m_e/m_mu);
  (5) records the quark c-coefficients NUMERICALLY at their natural exponent n.

HONEST RESIDUAL: the *exact rational* quark c's (the analog of the lepton 16/7)
require the exact transport amplitudes Lambda_{f,j} in closed form, i.e. the
off-diagonal SU(3)_F holonomy U_f* of nabla_F* -- a finite but genuinely analytic
Paper-3 step.  The table Lambda are 3-digit derived values, so only the *ratios*
(which cancel the normalization) are pinned exactly here.
"""
import mpmath as mp
from tfpt_constants import check, summary, reset, phi0

mp.mp.dps = 30
lY = mp.sqrt(phi0 * (1 - phi0))

# Paper-3 theorem outputs: field -> (word-length L, transport amplitude Lambda)
TAB = {
    'e': (8, '0.466'), 'mu': (5, '1.085'), 'tau': (3, '0.899'),
    'u': (7, '0.440'), 'd': (7, '0.936'), 's': (5, '0.943'),
    'c': (3, '0.646'), 'b': (2, '0.480'), 't': (0, '0.986'),
}


def yuk(f):
    L, Lam = TAB[f]
    return lY**L * mp.mpf(Lam)


def run():
    reset()
    print("v18  charged-fermion Yukawa sector + quark c-readout (A4)")
    check("lambda_Y = sqrt(phi0(1-phi0)) ~ 0.2244", lY, mp.mpf('0.22438'), tol=mp.mpf('1e-3'))

    # (1) quark source ratios (theory-quoted closed-branch values)
    y = {f: yuk(f) for f in TAB}
    check("mu/md = Lambda_u/Lambda_d = 0.470085 (theory)", y['u'] / y['d'], mp.mpf('0.470085'), tol=mp.mpf('1e-5'))
    check("mc/ms = lY^-2 Lambda_c/Lambda_s = 13.61 (theory)", y['c'] / y['s'], mp.mpf('13.61'), tol=mp.mpf('2e-3'))
    check("mt/mb = lY^-2 Lambda_t/Lambda_b = 40.80 (theory)", y['t'] / y['b'], mp.mpf('40.80'), tol=mp.mpf('2e-3'))

    # (2) lepton c-form: lambda_Y^L Lambda = pi c phi0^n  (validates the framework)
    for f, n, c in [('e', 5, mp.mpf(16) / 7), ('mu', 3, mp.mpf(4) / 3), ('tau', 2, mp.mpf(7) / 6)]:
        cc = y[f] / (mp.pi * phi0**n)
        check(f"lepton c_{f} ~ {mp.nstr(c,5)} (table-Lambda rounding, 2%)", cc, c, tol=mp.mpf('2.5e-2'))

    # (3) full hierarchy ordering (intrinsic Yukawas, all distinct and correctly ordered)
    up = [y['t'], y['c'], y['u']]
    dn = [y['b'], y['s'], y['d']]
    lep = [y['tau'], y['mu'], y['e']]
    check("up-sector ordering y_t > y_c > y_u", up == sorted(up, reverse=True))
    check("down-sector ordering y_b > y_s > y_d", dn == sorted(dn, reverse=True))
    check("lepton ordering y_tau > y_mu > y_e", lep == sorted(lep, reverse=True))
    check("cross-sector: y_t (top) is the unique O(1) anchor (L=0)", y['t'] > mp.mpf('0.5') and max(up[1:] + dn + lep) < mp.mpf('0.05'))

    # (4) match to observed (PDG) ratios where comparison is scheme-light
    check("mu/md ~ observed 0.47 (PDG MSbar 2 GeV ~0.46)", y['u'] / y['d'], mp.mpf('0.47'), tol=mp.mpf('5e-2'))
    check("mc/ms ~ observed 13.6 (PDG MSbar ~13.6)", y['c'] / y['s'], mp.mpf('13.6'), tol=mp.mpf('5e-2'))
    check("m_mu/m_tau = (8/7)phi0 ~ observed 0.0595", y['mu'] / y['tau'], mp.mpf('105.66') / mp.mpf('1776.86'), tol=mp.mpf('3e-2'))
    check("m_e/m_mu = (12/7)phi0^2 ~ observed 0.00484", y['e'] / y['mu'], mp.mpf('0.510999') / mp.mpf('105.66'), tol=mp.mpf('3e-2'))

    # (5) record quark c-coefficients at the natural exponent (numerical; exact forms open)
    qn = {'t': 0, 'c': 2, 'u': 4, 'b': 2, 's': 3, 'd': 4}
    print("      quark c-readout  c = lambda_Y^L Lambda /(pi phi0^n)  [numerical; exact rationals need U_f*]:")
    for f in ['t', 'c', 'u', 'b', 's', 'd']:
        cc = y[f] / (mp.pi * phi0**qn[f])
        print(f"        c_{f} (n={qn[f]}) = {mp.nstr(cc, 6)}")
    return summary("v18 quark Yukawa sector")


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