"""master/hadrons — a ledger file of the master's block G, the hadron rows: the rows the hadrons theme proves (the master's
witnesses, 19 October 2026).

The master's hadron rows of block G are bound by this file (the hadrons theme above the interactions theme's colour
sector). It binds G8 (the hadron spectrum: the baryon as the centre-neutral triality invariant and the SU(3)_F relations
as scale-cancelling identities), G9 (the residue series: baryon 1, meson 1, with photon 2 and gluon 0) and G10 (the
baryon scale: the exact spin split and Λ–N gap, the finite-stage eigenvalues exact by Sturm's count, the computed
eigenvalue E₀ read against the nucleon): the table of keys (generated from docs/00-ledger.json by ci/make_ledgers.py),
the Lean proofs each key conjoins (PROOFS), and the checks, which call the hadrons theme (frc/hadrons.py) and, for the
readings of G10, the chart theme (frc/chart_hadrons.py). The Lean side is lean/FrcCore/Theme/Hadrons.lean, the key file
lean/FrcCore/Keys/Hadrons.lean and the certificate lean/FrcCore/Ledgers/Master/Hadrons.lean. G10 is a T row of block G,
so its key is the core's (its chart readings stay the row's confrontation, decided here in the python check alone; gate G08).

    python3 -m frc.ledgers.master.hadrons        every block, the census; exit 1 if a check fails (≈ 4 s)

Blocks:  S  the hadron spectrum: the colour frame, the identities, the colour–spin–charge arithmetic   EXACT  (00:G8)
         R  the residue series: baryon 1 by the determinant, meson 1 by the contraction            EXACT  (00:G9)
         B  the baryon scale: the exact split and gap, Sturm's count, E₀ against the nucleon        CHART  (00:G10)

The notebook frc/ledgers/master/hadrons.ipynb runs one row per cell, the cell's id its key (gate G13).
"""
import sys
from fractions import Fraction as Q
from math import comb

from frc.registry import Registry
from frc import interactions as I
from frc import hadrons as H
from frc import chart_hadrons as CH

# ---- generated by ci/make_ledgers.py from docs/00-ledger.json; edit the ledger, not this table ----
BLOCK = "G"
KEYS = {"G1": "p00178", "G2": "p00067", "G3": "p00068", "G4": "p00069", "G5": "p00070", "G6": "p00071", "G7": "p27043", "G8": "p00073", "G9": "p00074", "G10": "p00075", "G11": "p27020", "G12": "p00155", "G13": "p00078", "G14": "p00079", "G15": "p00080", "G16": "p00081", "G17": "p00179", "G18": "p00083", "G19": "p00088", "G20": "p00089", "G21": "p00090"}       # every row of the block: its label and its accession key
LEAN = {"G8": "core", "G9": "core", "G10": "core"}       # the rows with a Lean declaration: the libraries whose key files prove them
# ---- end of the generated table ----

# The Lean proofs of the rows' keys: the theorems of the themes that each key conjoins (lean/make_keys.py writes the keys
# FRC.Ledger.p<key> from them). The master's block file is the binding's source, as a paper's \lean{} cells are its own.
PROOFS = {
    "G8": ["FRC.Hadrons.colour_group", "FRC.Hadrons.colourless_content", "FRC.Hadrons.gmo", "FRC.Hadrons.spacing",
           "FRC.Hadrons.coleman_glashow", "FRC.Hadrons.charge_structure", "FRC.Hadrons.sigma_lambda",
           "FRC.Hadrons.vector_spacing", "FRC.Hadrons.spin_pattern", "FRC.Hadrons.colour_factor",
           "FRC.Hadrons.adjoint_channel"],            # 35:C1, C15, C2, C3, C7, C8, C9, C18, C5, C4, C6/C14; heavy-quark symmetry (35:C10) is a Mathlib reading, no core clause
    "G9": ["FRC.Hadrons.colourless_content", "FRC.Hadrons.meson_invariant"],                       # 35:C15, 35:C18
    "G10": ["FRC.Hadrons.spin_split", "FRC.Hadrons.lambda_n_gap", "FRC.Hadrons.airy_sturm"],      # 35:C17, C19, C16: the exact clauses of the baryon scale
}

LEAN_ONLY = ()                  # the rows with a Lean declaration and no python check (gate G12): none

LEDGER = {"S1": "00:G8", "S2": "00:G8", "S3": "00:G8", "R1": "00:G9", "B1": "00:G10", "B2": "00:G10"}
BLOCKS = {"S": "the hadron spectrum: the colour frame, the identities, the colour–spin–charge arithmetic",
          "R": "the residue series: baryon 1 by the determinant, meson 1 by the contraction",
          "B": "the baryon scale: the exact split and gap, Sturm's count, E₀ against the nucleon"}
PREDICATES = {"00:G8": "S1", "00:G9": "R1", "00:G10": "B1"}

R = Registry("00", "hadrons", LEDGER, PREDICATES, sources=[__file__])


def _within(x, centre, tol):
    return abs(Q(x) - Q(centre)) < Q(tol)


def _between(x, lo, hi):
    return Q(lo) < Q(x) < Q(hi)


# ------------------------------------------------------------------------------------------------------------
# block S: the hadron spectrum (00:G8)
@R.block("S", BLOCKS["S"])
def block_S():
    """Block S — the hadron spectrum (EXACT): S1 the frame and the identities, S2 the arithmetic, S3 the hyperfine channel."""
    # 00:G8 (p00073)
    F, G = H.colour_group()
    scal = H.colour_scalars(F); cen = H.centre(F, G); content = H.colourless_content(F, G)
    frame = len(G) == 216 and sorted(cen) == sorted(scal) and len(scal) == 3 and content == (1, 0, 0, 1) and H.triality(3, 0) == 0
    gmo = H.gmo_vector(); d1, d2 = H.spacing_vectors(); cg = H.coleman_glashow(); v = H.vector_spacing()
    identities = gmo.is_zero() and d1.is_zero() and d2.is_zero() and cg.is_zero() and v.is_zero()
    qp = [H.QUARK_CHARGE[q] for q in "uud"]; qn = [H.QUARK_CHARGE[q] for q in "udd"]
    (op, tp), (on, tn) = H.charge_structure(qp), H.charge_structure(qn)
    pc = H.pair_correlators()
    orderings = (op, tp) == (1, 0) and (on, tn) == (Q(2, 3), Q(-1, 3)) and op > on                   # M_n > M_p: the charge structure, m_d > m_u
    orderings &= pc["ud_spin1"] - pc["ud_spin0"] == 1 and pc["s_pair_sigma"] - pc["s_pair_lambda"] == -1    # M_Σ > M_Λ: a_ll(1 − m_l/m_s) > 0
    R.check("S1", "the hadron spectrum's exact content: a baryon is the centre-neutral triality invariant of SU(3, F_2) — the group "
            "built exactly over F_4 (216 elements, the centre the three scalars, Z_3) with the colourless content (1, 0, 0, 1) of "
            "Λ•(3), the determinant the one invariant (triality 0); the SU(3)_F mass relations are zero polynomials in their "
            "parameters, scale-cancelling: Gell-Mann–Okubo 2N + 2Ξ − 3Λ − Σ, the decuplet's two second differences, "
            "Coleman–Glashow (n − p) + (Ξ⁻ − Ξ⁰) − (Σ⁻ − Σ⁺), the vector nonet's 2K* − ρ − φ; the orderings M_n > M_p (the "
            "charge structure Σ Q² = 1 against 2/3, two-body 0 against −1/3) and M_Σ > M_Λ (the light pair's S_u·S_d +1/4 "
            "against −3/4, the strange coupling −1 against 0, M_Σ − M_Λ = a_ll(1 − m_l/m_s) > 0)",
            frame and identities and orderings,
            f"|SU(3, 2)| = {len(G)}, content {content}; GMO {gmo}, spacing {d1}, {d2}, CG {cg}, nonet {v}; p ({op}, {tp}), n ({on}, {tn})")
    c2, sTT, sll, per = H.colour_factor(); e8, e10, sep, de = H.hyperfine_eigenvalues()
    ok = c2 == Q(4, 3) and sTT == -2 and sll == -8 and per == Q(-8, 3)
    ok &= H.g_spin(1) == Q(-3, 4) and H.g_spin(3) == Q(3, 4) and sep == Q(3, 2) and e8 == 2 and e10 == -2 and de == -4
    R.check("S2", "the colour–spin arithmetic of the hyperfine: the singlet's colour factor Σ λ_i·λ_j = −8 (−8/3 per pair) from "
            "C₂(3) = 4/3 and C₂(1) = 0; g_spin = ½S(S+1) − 9/8 is −3/4 on the octet and +3/4 on the decuplet, the separation 3/2; "
            "the eigenvalues of Σ(λ·λ)(S·S) on the singlet +2 and −2: M_10 − M_8 = (3/2)A_light, the decuplet heavier", ok,
            f"C₂ = {c2}, Σλ·λ = {sll}; g = {H.g_spin(1)}, {H.g_spin(3)}; eigenvalues {e8}, {e10}")
    E, c = H.weyl_moments(); c1, cadj = H.character_coefficients(3)
    ok = c["adjoint_in_3x3bar"] == 1 and c["adjoint_in_3x3"] == 0 and c["singlet_3x3bar"] == 1 and c["singlet_3x3"] == 0
    ok &= c1 == Q(1, 18) and cadj == Q(1, 36) and E[(1, 1)] == 1 and E[(2, 0)] == 0 and E[(2, 2)] == 2 and E[(3, 1)] == 0
    R.check("S3", "the decuplet–octet hyperfine is the colour-magnetic curvature invariant: by the Weyl constant terms the adjoint 8 "
            "sits once in 3 ⊗ 3̄ (E[χ²χ̄²] − E[χχ̄] = 1) and not in 3 ⊗ 3 (E[χ³χ̄] − E[χ²] = 0), so A_light = √σ c_mag(β) enters at "
            "O(β²) with c_adj = β²/36, the spin-2 partner of the tension's c₁ = β/18 (G5); the dimensionless pattern exact, the "
            "scale √σ the imported Ω-hard one", ok, f"moments {dict((k, v) for k, v in E.items() if k in [(1, 1), (2, 0), (2, 2), (3, 1)])}; c₁ {c1} β, c_adj {cadj} β²")


# ------------------------------------------------------------------------------------------------------------
# block R: the residue series (00:G9)
@R.block("R", BLOCKS["R"])
def block_R():
    """Block R — the residue series (EXACT): R1."""
    # 00:G9 (p00074)
    F, G = H.colour_group()
    content = H.colourless_content(F, G); E, c = H.weyl_moments()
    ok = content == (1, 0, 0, 1) and [comb(3, k) for k in range(4)] == [1, 3, 3, 1]           # no invariant vector of 3: the gluon's frame leaves a quark residue 0
    ok &= all(I.det(F, g) == F.one for g in G) and H.hermitian_invariant(F, G)                    # Λ³ = det fixed by every element; g†g = I: the q q̄ contraction invariant
    ok &= c["singlet_3x3bar"] == 1 and c["singlet_3x3"] == 0 and H.triality(3, 0) == 0 and H.triality(1, 1) == 0 and H.triality(1, 0) == 1
    R.check("R1", "the residue series closes: on SU(3, F_2) no nonzero vector of the fundamental is fixed (residue 0 for a single "
            "quark, the gluon frame's), none of Λ²(3), and Λ³(3) = det is fixed by every element — the baryon is the Carrier "
            "residue 1 at k = N = 3, forced; g†g = I on every element makes the q q̄ contraction the one invariant of 3 ⊗ 3̄ "
            "(E[χχ̄] = 1, E[χ²] = 0) — the meson is residue 1 with triality 1 + 2 ≡ 0, B = 0; with the photon's 2 and the "
            "gluon's 0 (G1, G4) the series is photon 2, gluon 0, baryon 1, meson 1; the stability selector is the "
            "realisation 35:B5", ok, f"content {content}, E[χχ̄] = {E[(1, 1)]}, E[χ²] = {E[(2, 0)]}")


# ------------------------------------------------------------------------------------------------------------
# block B: the baryon scale (00:G10)
@R.block("B", BLOCKS["B"])
def block_B():
    """Block B — the baryon scale: B1 chart (the exact clauses inside it), B2 the exact brackets."""
    # 00:G10 (p00075)
    gap = H.gap_identity(); s1, s2 = H.spin_split()
    exact = gap.is_zero() and s1.is_zero() and s2.is_zero()                                     # M_Λ − M_N = m_s − m_l; (M_N + M_Δ)/6 = λ_l, M_Δ − M_N = (3/2)λ_hf
    fl = CH.forward_landing(); ss = CH.single_scale(); t = CH.DATA["targets"]
    E0, E1 = fl["E0"], fl["E1"]; s = CH.DATA["scales"]["sqrt_sigma"]; mN = CH.pdg()["N"]
    MN_pred = Q(E0) * s; excess = (MN_pred - mN) / mN
    scale = _within(E0, "2.232", "0.001") and _between(MN_pred, "981", "983") and _between(excess, "0.045", "0.047")
    anchors = _between(ss["lam_l"], "0.822", "0.8224") and _between(ss["ms_over_ml"], "1.488", "1.489") and _between(ss["lam_hf"], "0.444", "0.4441")
    forward = abs(Q(fl["hf"]["lam_hf"]) - t["lam_hf"]) / t["lam_hf"] < Q("0.07") and abs(Q(fl["lam_l_fwd"]) - t["lam_l"]) / t["lam_l"] < Q("0.07")
    forward &= _between(fl["alpha_s"], "1.00", "1.01") and _within(fl["contact_nr"], 1, "0.002")
    R.check("B1", "[chart] the baryon scale: the spectrum is the Ω-hard √σ times sub-horizon numbers — the three anchored masses "
            "read as λ_l = 0.822, m_s/m_l = 1.489, λ_hf = 0.444 at √σ = 440 MeV, with M_Λ − M_N = m_s − m_l and the spin split "
            "inverting as exact identities; the baryon mass over scale is the computed finite eigenvalue E₀ = 2.232 of "
            "H = |p| + r on N = 600 sites, no baryon mass entering, M_N = E₀√σ = 982 MeV, 4.6 % above the nucleon; λ_l and λ_hf "
            "evaluated forward from {N = 3, β} (the contact |u'(0)|² → 1, α_s(√σ) = 2π/(9 ln 2) = 1.007) land within 7 % of the "
            "anchors: the light spectrum is parameter-free over √σ, no new Ω-hard residue",
            exact and scale and anchors and forward,
            f"E₀ = {CH.fmt(E0, 4)}, M_N = {CH.fmt(MN_pred, 0)} MeV ({CH.fmt(Q(excess) * 100, 1)} %); forward λ_hf {CH.fmt(fl['hf']['lam_hf'], 3)}, λ_l {CH.fmt(fl['lam_l_fwd'], 3)}",
            kind="CHART")
    br = [("2.33", "2.34"), ("4.08", "4.09"), ("5.51", "5.52"), ("6.77", "6.79")]
    counts = H.sturm_brackets(400, 20, br)
    R.check("B2", "the finite-stage eigenvalues are exact: Sturm's count of the tridiagonal H^(N) = −u'' + x u on N = 400 sites of "
            "[0, 20], in exact rational arithmetic, places exactly one eigenvalue in each of (2.33, 2.34), (4.08, 4.09), "
            "(5.51, 5.52) and (6.77, 6.79): the decimal Airy values are the [approx] readout of an exact finite spectrum",
            counts == [(k, k + 1) for k in range(4)], f"counts at the bracket ends {counts}")


if __name__ == "__main__":
    blocks = [a for a in sys.argv[1:] if a in R.blocks]
    if blocks:
        for b in blocks: R.run_block(b)
        sys.exit(0 if R.summary(write=False) else 1)
    sys.exit(0 if R.verify_all() else 1)