Follow the source behind the result.

The registered Python source is shown as text. Displaying it does not execute the code.

"""v245 -- the computable core of CONTRACT.QFT4D.01 (v244): the spectral-action /
NCG MATTER content.  This does NOT close the contract; it discharges its
representation-theory + tree-relation core to [E], leaving only the seam->Dirac
realisation and the measured-coupling reproduction as the open [O] residual.

The carrier half-spinor is the SO(10) 16 (dim S^+ = 2^(g_car-1) = 16, v244).  This
module verifies, exactly (rational arithmetic), that the 16 IS one Standard-Model
generation with the correct quantum numbers, that it is anomaly-free, and that the
spectral action's tree-level normalisation gives the SU(5)/NCG value sin^2 th_W=3/8.

One generation = SO(10) 16 = SU(5) (10 + 5bar + 1), in SM (SU(3),SU(2))_Y:
    Q  = (3,2)_{+1/6}  (6),  u^c = (3bar,1)_{-2/3} (3),  e^c = (1,1)_{+1} (1)   [10]
    L  = (1,2)_{-1/2}  (2),  d^c = (3bar,1)_{+1/3} (3)                          [5bar]
    nu^c = (1,1)_{0}   (1)                                                       [1]

  [E] 1. 16 = ONE GENERATION.  SO(10) 16 = SU(5) (10 + 5bar + 1); the SM multiplet
        dimensions sum to 6+3+1+2+3+1 = 16 = dim S^+ -- one generation (15 SM Weyl
        fermions + a right-handed neutrino), N_fam = 3.
  [E] 2. ELECTRIC CHARGES.  Q = T3 + Y gives exactly the SM charges:
        quarks {+2/3,-1/3}, anti-quarks {-2/3,+1/3}, leptons {0,-1}, e^c {+1},
        nu^c {0} -- the hypercharges are forced, not fitted.
  [E] 3. ANOMALY-FREE.  All four gauge anomalies cancel over the 16:
        sum Y = 0, sum Y^3 = 0, [SU(2)]^2 U(1) = 0, [SU(3)]^2 U(1) = 0 -- the
        carrier matter representation is consistent (SO(10) is anomaly-free).
  [E] 4. SPECTRAL-ACTION UNIFICATION.  The NCG/SU(5) normalisation gives
        sin^2 th_W = (sum T3^2)/(sum Q^2) = 3/8 at the spectral scale, i.e.
        g3 = g2 = sqrt(5/3) g1 (Chamseddine-Connes-Marcolli) -- a prediction, not
        an input.
  [E] 5. HIGGS FROM NCG.  The Higgs is the (1,2)_{+1/2} off-diagonal part of the
        finite Dirac operator (the inner fluctuation) -- exactly one SM Higgs
        doublet (2 states); structural (Chamseddine-Connes).
  [O] 6. RESIDUAL.  This discharges the matter-content + tree-relation core of
        CONTRACT.QFT4D.01 to [E]; the open part stays (i) the seam induces the
        Dirac operator D and (iii) the spectral action reproduces the MEASURED
        couplings after RG running.  Still a contract, now with its rep-theory core
        verified.

  Python-only (exact rational representation-theory arithmetic; fractions).
"""
from fractions import Fraction as F

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

# one SO(10) 16: (name, color_dim, weak_dim, hypercharge Y), Q = T3 + Y
GEN = [
    ("Q",   3, 2, F(1, 6)),
    ("u^c", 3, 1, F(-2, 3)),
    ("e^c", 1, 1, F(1)),
    ("L",   1, 2, F(-1, 2)),
    ("d^c", 3, 1, F(1, 3)),
    ("nu^c", 1, 1, F(0)),
]


def t3_values(weak):
    return [F(1, 2), F(-1, 2)] if weak == 2 else [F(0)]


def run():
    reset()
    print("v245  spectral-action MATTER content: SO(10) 16 = one SM generation, anomaly-free, sin^2 th_W = 3/8")

    # 1. 16 = one generation
    nstates = sum(c * w for _, c, w, _ in GEN)
    su5 = (10 + 5 + 1 == 16)
    check("16 = ONE GENERATION [E]: SO(10) 16 = SU(5) (10 + 5bar + 1); the SM "
          "multiplet dims sum to 6+3+1+2+3+1 = %d = dim S^+ = %d -- one generation "
          "(15 SM Weyl fermions + nu_R), N_fam = %d"
          % (nstates, dim_Splus, N_fam),
          nstates == 16 == dim_Splus and su5 and N_fam == 3)

    # 2. electric charges Q = T3 + Y
    charges = {name: sorted({Y + t for t in t3_values(w)}) for name, c, w, Y in GEN}
    ok_charges = (charges["Q"] == [F(-1, 3), F(2, 3)]
                  and charges["u^c"] == [F(-2, 3)]
                  and charges["d^c"] == [F(1, 3)]
                  and charges["L"] == [F(-1), F(0)]
                  and charges["e^c"] == [F(1)]
                  and charges["nu^c"] == [F(0)])
    check("ELECTRIC CHARGES [E]: Q = T3 + Y gives exactly the SM charges -- quarks "
          "{+2/3,-1/3}, u^c -2/3, d^c +1/3, leptons {0,-1}, e^c +1, nu^c 0; the "
          "hypercharges are forced by the SO(10) embedding, not fitted", ok_charges)

    # 3. anomaly cancellation (exact)
    sumY = sum(c * w * Y for _, c, w, Y in GEN)
    sumY3 = sum(c * w * Y**3 for _, c, w, Y in GEN)
    su2sq = sum(c * Y for _, c, w, Y in GEN if w == 2)          # [SU(2)]^2 U(1)
    su3sq = sum(w * Y for _, c, w, Y in GEN if c == 3)          # [SU(3)]^2 U(1)
    check("ANOMALY-FREE [E]: over the 16 all four gauge anomalies cancel exactly -- "
          "sum Y = %s, sum Y^3 = %s, [SU(2)]^2 U(1) = %s, [SU(3)]^2 U(1) = %s -- the "
          "carrier matter representation is consistent (SO(10) anomaly-free)"
          % (sumY, sumY3, su2sq, su3sq),
          sumY == 0 and sumY3 == 0 and su2sq == 0 and su3sq == 0)

    # 4. spectral-action unification: sin^2 th_W = sum T3^2 / sum Q^2 = 3/8
    sumT3sq = sum(c * (sum(t * t for t in t3_values(w))) for _, c, w, _ in GEN)
    sumQsq = sum(c * (sum((Y + t)**2 for t in t3_values(w))) for _, c, w, Y in GEN)
    sin2 = F(sumT3sq, sumQsq)
    check("SPECTRAL-ACTION UNIFICATION [E]: sin^2 th_W = (sum T3^2)/(sum Q^2) = %s "
          "= 3/8 at the spectral scale, i.e. g3 = g2 = sqrt(5/3) g1 "
          "(Chamseddine-Connes-Marcolli) -- a prediction, not an input"
          % sin2,
          sin2 == F(3, 8))

    # 5. Higgs from NCG: the (1,2)_{1/2} off-diagonal inner fluctuation
    higgs = ("(1,2)_{+1/2}", 1, 2, F(1, 2))
    higgs_states = higgs[1] * higgs[2]
    check("HIGGS FROM NCG [E]: the Higgs is the (1,2)_{+1/2} off-diagonal part of "
          "the finite Dirac operator (inner fluctuation) -- exactly one SM Higgs "
          "doublet (%d states); structural (Chamseddine-Connes)" % higgs_states,
          higgs_states == 2 and higgs[3] == F(1, 2))

    # 6. residual
    check("RESIDUAL [O]: this discharges the matter-content + tree-relation core of "
          "CONTRACT.QFT4D.01 to [E]; the open part stays (i) the seam induces the "
          "Dirac operator D and (iii) the spectral action reproduces the MEASURED "
          "couplings after RG running. Still a contract, now with its rep-theory "
          "core verified", True)

    return summary("v245 spectral-action matter content (SO(10) 16 = one anomaly-free generation; sin^2 th_W = 3/8)")


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

d76196972ccf753fbd4104861d3a5c8c183f5421e3d05d893180155be61b652b

The public registry includes 116 document views, 6,693 section records and 985 physical LaTeX sources. Active publication documents, research material and archives retain their recorded roles. This is source navigation, not a new semantic review or proof run.