Follow the source behind the result.

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

"""v247 -- PS.E8BRANCH.01: the E8 audit hull forbids the 126 and supplies exactly
{1, 10, 16, 45} for SO(10).  This turns the phenomenological "16-Higgs preferred
over 126-Higgs" (the scalaron-match selection of the gauge-unification experiment)
into an ALGEBRAIC statement about the E8 compiler.

The carrier is D5 (+) A3 = SO(10) x SU(4) (= SO(10) x SO(6)), a rank-8 subalgebra
of E8 via SO(16).  The branching of the adjoint 248 is the standard chain
E8 -> SO(16) -> SO(10) x SO(6):

  248 = 120 (adj SO16) + 128 (spinor SO16)
      = [ (45,1) + (1,15) + (10,6) ]  +  [ (16,4) + (16bar,4bar) ]

So the SO(10) representations that occur in the E8 hull are EXACTLY {1, 10, 16, 45}
(and 16bar).  The rank-5 antisymmetric tensor 126 (dim 126) does NOT occur.

  [E] 1. RANKS: rank SO(10) + rank SU(4) = 5 + 3 = 8 = rank E8.
  [E] 2. DIMENSIONS: (45,1)+(1,15)+(10,6)+(16,4)+(16bar,4bar) = 45+15+60+64+64 = 248
        = dim E8; the SO(16) split is 120 = 45+15+60 (adjoint) and 128 = 64+64
        (spinor = spinor_SO10 (x) spinor_SO6).
  [E] 3. SO(10) CONTENT = {1, 10, 16, 45} (16bar conjugate); the 126 is ABSENT.
        Hence, IF the physical fields are E8-hull representations, the renormalisable
        126_H is algebraically FORBIDDEN -- the proton-safe content 10 + 16 + 45 is
        E8-supplied, not fitted.
  [E] 4. MULTIPLICITY CAVEAT (honest, falsifiable): the 248 supplies only ONE (45,1)
        and ONE (1,15).  The gauge-unification experiment's proton-safe corridor
        wanted ~2 SU(4)-adjoint (15,1,1) units, so the minimal E8-allowed content
        (one 45) is proton-MARGINAL, not comfortably safe -- a sharp constraint, not
        a knob.
  [O] 5. THE INPUT PRINCIPLE.  "All TFPT fields are E8-hull (248) representations"
        is the premise that forbids the 126; the independent NCG derivation (the
        Higgs content as inner fluctuations Omega^1_D of the seam Dirac operator,
        CONTRACT.QFT4D.DIRAC.01 / v250) is the [O] complement.

Status: [E] for the branching, the SO(10) content, the no-126 and the one-45
multiplicity; [O] for the field-content principle.  Python-only (rep-theory /
dimension arithmetic).
"""
from tfpt_constants import check, summary, reset, g_car, N_fam, rankE8

# E8 -> SO(10) x SU(4) branching of the 248: (SO10 dim, SU4 dim, label, SO16 origin)
BRANCHING = [
    (45, 1, "(45,1) adj SO(10)", "120"),
    (1, 15, "(1,15) adj SU(4)", "120"),
    (10, 6, "(10,6) vector x 6", "120"),
    (16, 4, "(16,4) spinor", "128"),
    (16, 4, "(16bar,4bar) spinor", "128"),
]


def run():
    reset()
    print("v247  PS.E8BRANCH.01: E8 hull forbids 126, supplies {1,10,16,45} for SO(10)")

    # 1. ranks
    check("RANKS [E]: rank SO(10) + rank SU(4) = 5 + 3 = %d = rank E8 = %d "
          "(carrier D5(+)A3 is a rank-8 subalgebra of E8 via SO(16))"
          % (5 + 3, rankE8),
          5 + 3 == rankE8 == 8 and g_car == 5 and N_fam == 3)

    # 2. dimensions + SO(16) split
    total = sum(a * b for a, b, _, _ in BRANCHING)
    adj_so16 = sum(a * b for a, b, _, o in BRANCHING if o == "120")
    spin_so16 = sum(a * b for a, b, _, o in BRANCHING if o == "128")
    check("DIMENSIONS [E]: (45,1)+(1,15)+(10,6)+(16,4)+(16bar,4bar) = "
          "45+15+60+64+64 = %d = dim E8; SO(16) split 120 (adjoint) + 128 (spinor) "
          "= %d + %d" % (total, adj_so16, spin_so16),
          total == 248 and adj_so16 == 120 and spin_so16 == 128)

    # 3. SO(10) content + no 126
    so10_reps = sorted(set(a for a, _, _, _ in BRANCHING))
    check("SO(10) CONTENT = {1,10,16,45} [E]: the SO(10) reps in the E8 hull are %s "
          "(16bar conjugate); the 126 (dim 126) is ABSENT -> the renormalisable "
          "126_H is algebraically forbidden if fields are E8-hull reps; 10+16+45 is "
          "E8-supplied, not fitted" % so10_reps,
          so10_reps == [1, 10, 16, 45] and 126 not in so10_reps)

    # 4. multiplicity caveat: only one 45, one 15
    n45 = sum(1 for a, b, _, _ in BRANCHING if a == 45 and b == 1)
    n15 = sum(1 for a, b, _, _ in BRANCHING if a == 1 and b == 15)
    check("MULTIPLICITY CAVEAT [E]: the 248 supplies only ONE (45,1) and ONE (1,15) "
          "(found %d, %d); the proton-safe corridor wanted ~2x SU(4)-adjoint, so the "
          "minimal E8-allowed content (one 45) is proton-MARGINAL -- a sharp "
          "falsifiable constraint, not a knob" % (n45, n15),
          n45 == 1 and n15 == 1)

    # 5. the input principle (typed open)
    check("INPUT PRINCIPLE [O]: 'all TFPT fields are E8-hull (248) reps' is the "
          "premise that forbids the 126; the NCG inner-fluctuation derivation "
          "(Omega^1_D of the seam Dirac operator, v250) is the independent complement",
          True)

    return summary("v247 E8 hull forbids 126, supplies {1,10,16,45} (PS.E8BRANCH.01)")


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

16a43f14e53db9a4815e6c854b22e164e779ca97b89ca6c0371a8dc5c6f9a090

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.