Follow the source behind the result.

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

"""v443 -- SEAM.E8.DISCRIMINATOR.01: the empirical/structural DISCRIMINATOR bundle
(mode D of the v347 closure-mode classification) -- concrete FALSIFIABLE kill tests
that separate the claimed seam = (E8)_1 from every nearby c=8 alternative.

v347 lists four closure modes for the one open arrow; mode D is "test the
consequences."  This module realises mode D as a bundle of sharp discriminators
against the nearest rival, SO(16)_1 = (D8)_1 (same central charge c=8, the v277
ambiguity).  Each is an [X] kill test: if the physical seam ever shows the rival's
signature, (E8)_1 is falsified.

  [E]/[X] 1. PRIMARY / GSD DISCRIMINATOR.  |det Cartan(E8)|=1 (ONE primary,
         holomorphic) vs |det Cartan(D8)=SO(16)|=4 (FOUR primaries 1,v,s,c); the
         torus ground-state degeneracy = #primaries = 1 (E8) vs 4 (SO(16)).
         KILL TEST: a seam with GSD>1 / >1 superselection sector falsifies (E8)_1.
  [E]/[X] 2. CURRENT / THETA DISCRIMINATOR.  level-1 current count dim E8=248 vs
         dim SO(16)=120; the E8 lattice theta has 240 norm-2 roots (=112 integer +
         128 spinor, computed) vs D8's 112 -- the affine current spectrum and the
         lattice theta DIFFER.  KILL TEST: the edge current multiplicity (248 vs
         120) is observable.
  [E] 3. c=8 IS NOT A DISCRIMINATOR.  both nets have c=8 (the v277 ambiguity), so
         the central charge alone CANNOT decide; only the order-4 mu4 condensation +
         det K=1 (the genus-1 statement, SEAM.S3.MODULAR.01/v90) selects E8.
  [E] 4. NON-VACUITY.  the discriminators all fire on the rival (det 4!=1, currents
         120!=248, roots 112!=240) -- the kill tests are non-vacuous.
  [X]/[C] 5. VERDICT.  the (E8)_1 seam carries sharp falsifiable signatures distinct
         from every nearby c=8 net (mode D of v347 realised as concrete kill tests).
         SEAM.EQUIV.01 stays [O]: the discriminators distinguish the TARGET but do
         not by themselves PROVE the seam realises it (continuum existence, residual
         [O]); they make the claim FALSIFIABLE.

Python-only (numpy; the det/root-count facts are Wolfram-mirrored via v89/v281/v422).
"""
import itertools

import numpy as np

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


def cartan_E8():
    return np.array([
        [2, 0, -1, 0, 0, 0, 0, 0], [0, 2, 0, -1, 0, 0, 0, 0],
        [-1, 0, 2, -1, 0, 0, 0, 0], [0, -1, -1, 2, -1, 0, 0, 0],
        [0, 0, 0, -1, 2, -1, 0, 0], [0, 0, 0, 0, -1, 2, -1, 0],
        [0, 0, 0, 0, 0, -1, 2, -1], [0, 0, 0, 0, 0, 0, -1, 2]], dtype=float)


def cartan_D8():
    C = 2 * np.eye(8)
    for i in range(7):
        C[i, i + 1] = C[i + 1, i] = -1
    C[6, 7] = C[7, 6] = 0
    C[5, 7] = C[7, 5] = -1                                   # D8 fork
    return C


def count_norm2_integer():
    """norm-2 vectors of the D8 (integer, even-sum) lattice: (+-1,+-1,0^6)."""
    n = 0
    for i, j in itertools.combinations(range(8), 2):
        for si in (1, -1):
            for sj in (1, -1):
                n += 1                                       # vector with +-1 at i,j
    return n                                                 # 28*4 = 112


def count_norm2_spinor():
    """norm-2 vectors in the (1/2)^8 spinor coset with even # of minus signs."""
    n = 0
    for signs in itertools.product((0.5, -0.5), repeat=8):
        if sum(1 for s in signs if s < 0) % 2 == 0:         # even minus signs
            if abs(sum(s * s for s in signs) - 2.0) < 1e-9:  # norm^2 = 8*1/4 = 2
                n += 1
    return n                                                 # 128


def run():
    reset()
    print("v443 SEAM.E8.DISCRIMINATOR: the mode-D empirical kill-test bundle "
          "(E8)_1 vs SO(16)_1")

    det_E8 = int(round(np.linalg.det(cartan_E8())))
    det_D8 = int(round(np.linalg.det(cartan_D8())))

    # ---- 1. primary / GSD discriminator ----
    gsd_E8, gsd_D8 = abs(det_E8), abs(det_D8)               # torus GSD = #primaries
    check("PRIMARY / GSD DISCRIMINATOR [E]/[X]: |det Cartan(E8)|=%d (ONE primary, "
          "holomorphic) vs |det Cartan(D8)=SO(16)|=%d (FOUR primaries 1,v,s,c); "
          "torus GSD = #primaries = %d vs %d. KILL TEST: a seam with GSD>1 / >1 "
          "superselection sector falsifies (E8)_1"
          % (det_E8, det_D8, gsd_E8, gsd_D8),
          det_E8 == 1 and det_D8 == 4)

    # ---- 2. current / theta discriminator ----
    dim_E8, dim_SO16 = 248, 120                             # level-1 current counts
    roots_int = count_norm2_integer()                       # 112 (D8 roots)
    roots_spin = count_norm2_spinor()                       # 128 (spinor coset)
    roots_E8 = roots_int + roots_spin                       # 240
    check("CURRENT / THETA DISCRIMINATOR [E]/[X]: level-1 currents dim E8=%d vs "
          "dim SO(16)=%d; E8 lattice theta has %d norm-2 roots (=%d integer + %d "
          "spinor, computed) vs D8's %d -- current spectrum and lattice theta DIFFER. "
          "KILL TEST: the edge current multiplicity (248 vs 120) is observable"
          % (dim_E8, dim_SO16, roots_E8, roots_int, roots_spin, roots_int),
          roots_int == 112 and roots_spin == 128 and roots_E8 == 240
          and dim_E8 == 240 + 8)

    # ---- 3. c=8 is NOT a discriminator ----
    c = g_car + N_fam
    check("c=8 IS NOT A DISCRIMINATOR [E]: both (E8)_1 and SO(16)_1 have c=%d (the "
          "v277 ambiguity), so the central charge ALONE cannot decide; only the "
          "order-4 mu4 condensation + det K=1 (the genus-1 statement, "
          "SEAM.S3.MODULAR.01/v90) selects E8" % c,
          c == 8)

    # ---- 4. non-vacuity ----
    fires = (det_D8 != det_E8) and (dim_SO16 != dim_E8) and (roots_int != roots_E8)
    check("NON-VACUITY [E]: the discriminators all fire on the rival (det %d!=%d, "
          "currents %d!=%d, roots %d!=%d) -- the kill tests are non-vacuous"
          % (det_D8, det_E8, dim_SO16, dim_E8, roots_int, roots_E8),
          fires)

    # ---- 5. verdict (typed [X]/[C]) ----
    check("VERDICT [X]/[C]: the (E8)_1 seam carries sharp falsifiable signatures "
          "distinct from every nearby c=8 net (mode D of v347 as concrete kill "
          "tests). SEAM.EQUIV.01 stays [O]: the discriminators distinguish the "
          "TARGET but do not by themselves PROVE the seam realises it (continuum "
          "existence, residual [O]); they make the claim FALSIFIABLE",
          det_E8 == 1 and det_D8 == 4 and roots_E8 == 240 and fires and g_car == 5)

    return summary("v443 SEAM.E8.DISCRIMINATOR (mode-D kill tests (E8)_1 vs SO(16)_1; "
                   "falsifiable; SEAM.EQUIV.01 stays [O])")


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

f105ba34437bfb765660daa837950322f1281012aafb062141e7209cfcc42876

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.