"""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)