Follow the source behind the result.

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

"""v286 -- SEAM.EQUIV.01: the Seam Equivalence contract.  This does NOT prove the
theorem; it FORCES the whole open structure onto a single named arrow and proves that
the two proof routes are non-circular (they may converge only through SEAM.EQUIV.01).

THE NAMED THEOREM (the one open statement of the structural core):
    Seam Equivalence Theorem (SEAM.EQUIV.01).  The raw reflection-positive seam state
    (gap, chirality, carrier clock) reconstructs canonically the SAME state as the
    holomorphic (E8)_1 boundary net at the tau=i pillowcase -- the equivalence
    respecting the DtN, the KMS modular flow, the mu4 deck, the Q-system extension,
    det K = 1 and the (E8)_1 character.  Short form: the raw seam IS (E8)_1 at tau=i.

Four objects and their arrows (a commuting square with one open diagonal):
    RawRPSeam --[i, open]--> FlatTauIPillowcaseDtN --[closed, Route i]--> omega o rho = omega
    RawRPSeam --[ii, open]--> SREKitaevE8Phase    --[closed, Route ii]--> HolomorphicE8Net
    FlatTauIPillowcaseDtN <--[conditional, v282]--> HolomorphicE8Net   (at tau=i)
    RawRPSeam ===========[THE GRAL]===========> HolomorphicE8Net  = SEAM.EQUIV.01

  [E] 1. FOUR OBJECTS TYPED.  RawRPSeam (RP data + gap + chirality + carrier clock),
        FlatTauIPillowcaseDtN (geometry route), HolomorphicE8Net (AQFT/RCFT route),
        SREKitaevE8Phase (topological phase, det K=1) -- the corners of the square.
  [E] 2. SIX ARROWS TYPED.  two CLOSED (Route i: FlatDtN -> omega o rho = omega,
        v276/v280/v284; Route ii: SRE -> HolomorphicE8Net, v281/v277/v235), one
        CONDITIONAL (FlatDtN <-> HolomorphicE8Net at tau=i, v282), and the open
        arrows (RawRPSeam -> FlatDtN, RawRPSeam -> SRE) which are the SAME open lemma
        (v284/v285 coincidence) = the Gral RawRPSeam -> HolomorphicE8Net.
  [E] 3. IMPORT FIREWALL (anti-circularity).  no Route-i module
        (v276/v280/v284) imports any Route-ii module (v277/v281/v285) or vice versa
        -- the two routes converge ONLY through this contract, so E8 cannot be
        smuggled into the geometry and pulled back out (the reviewer's worst attack).
  [E] 4. EXACT-LABEL TAXONOMY.  each arrow carries one of {Formal Exact (Lean),
        Numerical Exact (reproducible experiment), Conditional Exact (standard
        theorem under a stated premise), Open Selection (the theory-selection
        premise)} -- so a conditional arrow can never be misread as a proof.
  [O] 5. THE ONE OPEN ARROW.  exactly one arrow is Open Selection: RawRPSeam -> (its
        geometry/holomorphy image).  Proving the single arrow
        'free Gaussian RP bulk => holomorphic single-sector boundary net' closes the
        structural core; everything else is closed or conditional.

Status: [E] the typing + the import firewall + the exact-label taxonomy + the
single-open-arrow certificate; [O] the named theorem stays open.  A contract that
concentrates the whole open structure on one arrow; it does NOT prove it.  Writes
seam_equivalence.json.  Python (stdlib).
"""
import json
import os
import re

from tfpt_constants import check, summary, reset

HERE = os.path.dirname(os.path.abspath(__file__))

ROUTE_I = ["v276_qgeo_flat_closes_commutator", "v280_pillowcase_steklov",
           "v284_route_i_rp_uniqueness"]
ROUTE_II = ["v277_seam_calderon_e8_match", "v281_holomorphy_modular_data",
            "v285_route_ii_seam_condensation"]

OBJECTS = {
    "RawRPSeam": "RP data + gap + chirality + carrier clock (the primitive)",
    "FlatTauIPillowcaseDtN": "the geometry route image (flat tau=i Steklov DtN)",
    "HolomorphicE8Net": "the AQFT/RCFT route image (holomorphic (E8)_1 net)",
    "SREKitaevE8Phase": "the topological phase (short-range-entangled, det K=1)",
}

# arrow: (frm, to, status, label, evidence)
ARROWS = [
    ("RawRPSeam", "FlatTauIPillowcaseDtN", "open", "Open Selection", "the geometry premise"),
    ("FlatTauIPillowcaseDtN", "omega o rho = omega", "closed", "Numerical+Formal Exact",
     "Route i: v276/v280 + Lean FORM.QGEO.04; v284"),
    ("RawRPSeam", "SREKitaevE8Phase", "open", "Open Selection", "the SRE premise"),
    ("SREKitaevE8Phase", "HolomorphicE8Net", "closed", "Conditional+Formal Exact",
     "Route ii: v235/v277/v281; v285"),
    ("FlatTauIPillowcaseDtN", "HolomorphicE8Net @ tau=i", "conditional", "Conditional Exact",
     "v282: chi_E8(i)=12, the order-4 CM point = the (E8)_1 modulus"),
    ("RawRPSeam", "HolomorphicE8Net", "gral", "Open Selection",
     "SEAM.EQUIV.01 -- the one open arrow; = both open arrows above (v284/v285 coincide)"),
]


def _imports(mod):
    src = open(os.path.join(HERE, mod + ".py"), encoding="utf-8").read()
    return set(re.findall(r"(?:^import|^from)\s+(v\d+\w*)", src, re.MULTILINE))


def run():
    reset()
    print("v286  SEAM.EQUIV.01: the Seam Equivalence contract (concentrates the open structure on one arrow)")

    # 1. four objects
    check("FOUR OBJECTS TYPED [E]: %s -- the corners of the equivalence square"
          % ", ".join(OBJECTS), len(OBJECTS) == 4)

    # 2. six arrows: 2 closed, 1 conditional, the open arrows + the gral
    closed = [a for a in ARROWS if a[2] == "closed"]
    conditional = [a for a in ARROWS if a[2] == "conditional"]
    opens = [a for a in ARROWS if a[2] == "open"]
    gral = [a for a in ARROWS if a[2] == "gral"]
    check("SIX ARROWS TYPED [E]: %d closed (Route i + Route ii), %d conditional "
          "(v282), %d open premises (the SAME lemma, v284/v285), 1 Gral "
          "(SEAM.EQUIV.01)" % (len(closed), len(conditional), len(opens)),
          len(closed) == 2 and len(conditional) == 1 and len(opens) == 2 and len(gral) == 1)

    # 3. import firewall: routes do not import each other
    i_imports = set().union(*(_imports(m) for m in ROUTE_I))
    ii_imports = set().union(*(_imports(m) for m in ROUTE_II))
    i_to_ii = i_imports & set(ROUTE_II)
    ii_to_i = ii_imports & set(ROUTE_I)
    check("IMPORT FIREWALL [E]: no Route-i module (%s) imports any Route-ii module "
          "and vice versa (i->ii: %s, ii->i: %s) -- the routes converge ONLY through "
          "SEAM.EQUIV.01, so E8 cannot be smuggled into the geometry and pulled back "
          "out (the reviewer's worst attack)"
          % ("/".join(m.split("_")[0] for m in ROUTE_I), i_to_ii or "none", ii_to_i or "none"),
          not i_to_ii and not ii_to_i)

    # 4. exact-label taxonomy
    labels = {a[3] for a in ARROWS}
    allowed = {"Open Selection", "Numerical+Formal Exact", "Conditional+Formal Exact",
               "Conditional Exact"}
    check("EXACT-LABEL TAXONOMY [E]: every arrow carries a label in {Formal Exact, "
          "Numerical Exact, Conditional Exact, Open Selection} (used: %s) -- a "
          "conditional arrow can never be misread as a proof" % sorted(labels),
          labels <= allowed)

    # 5. the one open arrow
    check("THE ONE OPEN ARROW [O]: exactly one Gral arrow (RawRPSeam -> "
          "HolomorphicE8Net = SEAM.EQUIV.01); proving 'free Gaussian RP bulk => "
          "holomorphic single-sector boundary net' closes the structural core -- "
          "everything else is closed or conditional", len(gral) == 1)

    # write the machine-readable contract
    out = {
        "theorem": "SEAM.EQUIV.01",
        "statement": "the raw RP seam state reconstructs canonically the holomorphic "
                     "(E8)_1 boundary net at the tau=i pillowcase",
        "short_form": "the raw seam is (E8)_1 at tau=i",
        "objects": OBJECTS,
        "arrows": [{"from": a[0], "to": a[1], "status": a[2], "label": a[3],
                    "evidence": a[4]} for a in ARROWS],
        "import_firewall": {"route_i": ROUTE_I, "route_ii": ROUTE_II,
                            "i_imports_ii": sorted(i_to_ii), "ii_imports_i": sorted(ii_to_i),
                            "clean": not i_to_ii and not ii_to_i},
        "the_one_open_arrow": "free Gaussian RP bulk => holomorphic single-sector boundary net",
        "not_closed_by_this": ["v_geo (metrology primitive)", "F_transfer (downstream)",
                               "QG.AMB.01 (nonperturbative ambient measure)"],
    }
    with open(os.path.join(HERE, "seam_equivalence.json"), "w", encoding="utf-8") as f:
        json.dump(out, f, indent=2)

    return summary("v286 SEAM.EQUIV.01 contract: 4 objects, 6 arrows (2 closed + 1 conditional + 1 open Gral), import firewall clean, one open arrow")


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

8f3150d4dd1cd1f90ad7f705f8cf867e935bea7c066167f25d4c56bd55f3ba79

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.