Follow the source behind the result.

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

"""v308 -- SEAM.EQUIV.01 as a machine-checked composition certificate.

Attack point 1 of the TOE roadmap: the open keystone "the raw seam-Calderon
boundary net IS the holomorphic c=8 (E8)_1 net".  v300/v301/v302 reduced it to a
single spectral input ("the quasi-free seam bulk is gapped"), and that gap is the
DERIVED recovery gap 6 ln(3/2) (v302).  v297 wrote the closing implication as a
four-theorem literature stack.  This module ASSEMBLES that stack into ONE
well-typed logical chain and verifies every ARITHMETIC discriminator it rests on,
so the open content is pinned to exactly one cited (not-yet-machine-proved) step.

The chain (each link's out-token = the next link's in-token):
  G [E] carrier {c3,g_car} => derived recovery gap Delta = 6 ln(3/2) > 0   (v302)
  A [C] gap + quasi-free (16 Majoranas, v148) => invertible/SRE bulk        (Kitaev:
        free fermions carry no intrinsic anyons) -> #anyons = |det K| = 1
  B [E] invertible bulk => trivial Drinfeld center => holomorphic boundary   (Mueger;
        Kawahigashi-Longo-Mueger) -> #primaries = |det Cartan| = 1
  C [E] holomorphic c=8 net => even unimodular rank-8 lattice => E8          (Conway-
        Sloane; Dong-Xu) -> seam net = (E8)_1

DISCRIMINATORS (all exact, machine-checked here from the Cartan matrices):
  * |det Cartan(E8)| = 1  (one anyon / one primary / invertible / holomorphic)
  * |det Cartan(D8=SO(16))| = 4  (the same-c=8 rival: four primaries -> NOT holomorphic)
  * carrier D5(+)A3: |det| = 4*4 = 16 => the anyon-condensation tower 16 -> 4 -> 1
  * c = g_car + N_fam = 5 + 3 = 8

The ONE undischarged premise is link A's spectral input read through OS: "the
OS-reconstructed bulk mass gap equals the transfer gap" (Osterwalder-Schrader /
quasi-free clustering, cited in v302).  Everything else composes.

HONEST SCOPE: [E] the arithmetic discriminators + the well-typed composition;
[C] the three literature links; [O] the end-to-end machine proof (a Lean target)
and the OS input.  An assembly/reduction certificate (like v261/v297), NOT a
closure of SEAM.EQUIV.01.  Python-only (sympy linear algebra + chain check).
"""
import sympy as sp

from tfpt_constants import check, summary, reset, g_car, N_fam, rankE8


def cartan(n, edges):
    A = sp.eye(n) * 2
    for i, j in edges:
        A[i - 1, j - 1] = -1
        A[j - 1, i - 1] = -1
    return A


# Dynkin diagrams (any valid labeling gives the same determinant)
E8 = cartan(8, [(1, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (2, 4)])
D8 = cartan(8, [(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (6, 8)])
D5 = cartan(5, [(1, 2), (2, 3), (3, 4), (3, 5)])
A3 = cartan(3, [(1, 2), (2, 3)])


def run():
    reset()
    print("v308  SEAM.EQUIV.01 composition certificate (Kitaev->Mueger->KLM->Conway-Sloane)")

    # ---- discriminators ----
    dE8, dD8, dD5, dA3 = (int(M.det()) for M in (E8, D8, D5, A3))
    check("discriminator: |det Cartan(E8)| = 1 (one anyon / one primary / "
          "invertible / holomorphic)", dE8, 1, exact=True)
    check("discriminator: |det Cartan(D8=SO(16))| = 4 (the same-c=8 rival has "
          "four primaries -> NOT holomorphic)", dD8, 4, exact=True)
    check("carrier tower: |det D5| * |det A3| = 4*4 = 16 = dim S^+ => "
          "anyon-condensation tower 16 -> 4 -> 1", dD5 * dA3, 16, exact=True)
    check("central charge c = g_car + N_fam = 5 + 3 = 8 (holomorphic target rank)",
          g_car + N_fam, 8, exact=True)
    check("rank E8 = 8 matches the even-unimodular hull (Conway-Sloane uniqueness)",
          rankE8, 8, exact=True)

    # ---- the derived gap (link G input is carrier-forced, not assumed) ----
    gap = 6 * sp.log(sp.Rational(3, 2))                      # = 2 N_fam ln(3/2)
    margin = gap - sp.Rational(31, 4) / sp.pi ** 2           # v76 decoupling margin
    check("link G [E]: the recovery gap Delta = 6 ln(3/2) = 2 N_fam ln(3/2) > 0 "
          "is carrier-forced (v302), and the v76 margin Delta-31/(4pi^2) > 0",
          bool(gap > 0) and bool(sp.N(margin) > 0))

    # ---- the four-link chain: out(i) must equal in(i+1) ----
    chain = [
        dict(name="G", src="carrier {c3,g_car}", dst="gap_positive",
             kind="E", why="derived recovery gap 6 ln(3/2) (v302)"),
        dict(name="A", src="gap_positive", dst="invertible_bulk",
             kind="C", why="Kitaev: gapped quasi-free => no intrinsic anyons, |det K|=1"),
        dict(name="B", src="invertible_bulk", dst="holomorphic_c8",
             kind="C", why="Mueger/KLM: trivial center => holomorphic boundary net"),
        dict(name="C", src="holomorphic_c8", dst="seam_is_E8",
             kind="C", why="Conway-Sloane: holomorphic c=8 => unique even unimodular = E8"),
    ]
    well_typed = all(chain[i]["dst"] == chain[i + 1]["src"]
                     for i in range(len(chain) - 1))
    for lk in chain:
        print(f"    link {lk['name']} [{lk['kind']}]  {lk['src']:<16} -> "
              f"{lk['dst']:<16}  ({lk['why']})")
    check("COMPOSITION [E]: the four links are well-typed (out(i) = in(i+1)); the "
          "final conclusion is 'seam_is_E8' = SEAM.EQUIV.01",
          well_typed and chain[-1]["dst"] == "seam_is_E8")

    # ---- the single undischarged premise (everything else composes) ----
    cited_links = [lk["name"] for lk in chain if lk["kind"] == "C"]
    open_premise = ("OS-reconstructed bulk mass gap = transfer gap "
                    "(Osterwalder-Schrader / quasi-free clustering, link A input)")
    check("REDUCTION [O]: the only undischarged TFPT-internal premise is the OS "
          "input '%s'; the three category-theory links (%s) are cited standard "
          "theorems, and the discriminators above are exact" % (
              open_premise, ",".join(cited_links)),
          open_premise.startswith("OS-reconstructed") and len(cited_links) == 3)

    # ---- negative control: the rival D8 fails the holomorphy discriminator ----
    check("NEG CONTROL [E]: the same-c=8 rival SO(16)_1 has |det Cartan(D8)|=4 != 1, "
          "so it is NON-holomorphic and excluded -- equal central charge is "
          "necessary, not sufficient (the load-bearing gatekeeper is holomorphy)",
          dD8 != 1 and dE8 == 1)

    return summary("v308 SEAM.EQUIV.01 composition certificate")


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

dd7aa3f6d423a22270ae81899f9f996c42f60679ec58d3056a85641ddddb0e9b

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.