A registered result in its source context
Original ledger classification: Machine [E] cohomology/census + [E-float] S rates and exact T + data-backed [C] B-vs-C3 pick (hardened by v652) (Python-only per GATE.WOLFRAM.02).
Recorded statement: The full Z3-orbifold assembly of the seam (one module, 17 checks, ~35 s; discovery probe orbifold_assembly_probe.py 17/17, verdict ORB-ASSEMBLY-SEAM). COHOMOLOGY [E]: H^2(Z3, U(1)) = 0 by machine enumeration (27 mu3-valued 2-cocycles = 9…
Statement, assumptions and sources
Paper context: input 5 tfpt 3 e8 audit bootstrap
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QGEO.ORBASM.01
Original ledger classification: Machine [E] cohomology/census + [E-float] S rates and exact T + data-backed [C] B-vs-C3 pick (hardened by v652) (Python-only per GATE.WOLFRAM.02).
Original claim text
The full Z3-orbifold assembly of the seam (one module, 17 checks, ~35 s; discovery probe orbifold_assembly_probe.py 17/17, verdict ORB-ASSEMBLY-SEAM). COHOMOLOGY [E]: H^2(Z3, U(1)) = 0 by machine enumeration (27 mu3-valued 2-cocycles = 9 coboundaries x 3 classes, every cocycle symmetric) -- NO discrete torsion for a pure Z3 orbifold; residual phase tables are exact charge-class relabelings. GRID [E]: all 35 nonvanishing Z6 sectors match |theta[gt/6,ht/6]/eta|^2 at < 1% (beyond v650: the odd deck powers). THE CENSUS [E, central]: of SIX assembly candidates the survivors of {integer spectrum, unique vacuum, S measured clean, T exact} are EXACTLY {B, C3} -- A (the naive Z3) dies by an exact T violation 3.5e-3 (= its charge-3 content: T kills the naive Z3 exactly), C1 by S stalling at 1.7e-3, C2 has no vacuum, A' by exact T violation 4.6e-1 AND the wrong first twisted exponent (5/18, not 1/9). THE PICK [E/C]: the seam data discriminate B from C3 -- B keeps every measured c = 0 sector ground and the Klein phase eta = (1,1) (v645); C3 excises all odd-sector grounds: THE SEAM ASSEMBLY IS B, the Z6 deck quotient with uniform charge-0 projection (data-backed [C] here; hardened structurally by v652). MEASURED [E]: the chiral phase e^{-2 pi i a~ b} (spectral-flow-reduced branch). GATE.QGEO does not move.
Original classification detail
ORB-ASSEMBLY-SEAM: H^2(Z3,U(1)) = 0 enumerated (no discrete torsion), six candidates -> exactly {B, C3} survive {integer spectrum, vacuum, S, T} (T kills the naive Z3 exactly at 3.5e-3), the seam data pick B (measured c = 0 grounds + Klein eta = (1,1)); chiral phase measured; GATE.QGEO does not move.
Dependencies as recorded
QGEO.ORBMOD.01; QGEO.KLEINRP.01; QGEO.TWISTOPE.01; v622; v623; v628; v639; v645
Open the original ledger source, row 654Location recorded in the ledger
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- E8 audit and bootstrap
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- Front matter / supportE8 audit and bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
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- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-10-18: Project separation and retained physics historyResearch changelog; TFPT — Introduction and reading guide
Registered verification modules
- v651_orbifold_assembly.pyRegistered verification module · core
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QGEO.ORBASM.01: der volle ℤ₃-Orbifold-Zusammenbau der Naht — **H²(ℤ₃, U(1)) = 0 PER MASCHINEN-ENUMERATION (27 Kozykel, alle symmetrisch: KEINE diskrete Torsion), UND VON SECHS KANDIDATEN ÜBERLEBEN {ganzzahliges Spektrum, eindeutiges Vakuum, S gemessen, T exakt} GENAU {B, C3}** — der naive ℤ₃ (A) stirbt an EXAKTER T-Verletzung 3.5e−3 (= sein Ladungs-3-Gehalt), C1 an S-Stau, C2 hat kein Vakuum, A' zusätzlich am falschen Twist-Exponenten (5/18 statt 1/9); **die Naht-Daten diskriminieren B von C3: B hält jeden gemessenen c = 0-Sektor-Grund und die Klein-Phase η = (1,1) — DER NAHT-ZUSAMMENBAU IST B** (ℤ₆-Deck-Quotient mit uniformer Ladungs-0-Projektion; datengestützt [C], v652 härtet strukturell); die chirale Phase e^{−2πi·ã·b} GEMESSEN (17 checks, ~35 s)
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