A registered result in its source context
Original ledger classification: Exact [E] sectors/characters/spin structure + [E-float] measured S-covariance (N^{-4}) + [C] typed continuum remainder (Python-only per GATE.WOLFRAM.02).
Recorded statement: The modular data of the Z3 orbifold of the seam on the lattice (one module, 17 checks, ~25 s; discovery probe orbifold_modular_probe.py 17/17, verdict ORB-MODULAR-COHERENT). SECTORS [E]: all nine twisted-sector partition functions Z[g,h]…
Statement, assumptions and sources
Paper context: input 5 tfpt 3 e8 audit bootstrap
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QGEO.ORBMOD.01
Original ledger classification: Exact [E] sectors/characters/spin structure + [E-float] measured S-covariance (N^{-4}) + [C] typed continuum remainder (Python-only per GATE.WOLFRAM.02).
Original claim text
The modular data of the Z3 orbifold of the seam on the lattice (one module, 17 checks, ~25 s; discovery probe orbifold_modular_probe.py 17/17, verdict ORB-MODULAR-COHERENT). SECTORS [E]: all nine twisted-sector partition functions Z[g,h] of the seam double (free complex fermion, N x L cylinder) are real positive with exact conjugation degeneracies and match the continuum |theta[g/3,h/3]/eta|^2 at < 1% on ln Z (N = 48; tau = i/2, i, 2i); the Casimir slopes reproduce the v628 coefficients per deck class (C_g/4 = (-1/24, 1/72, 1/72)). S MEASURED [E-float, central]: modular S-covariance converges with a clean common N^{-4} rate (4.06-4.32 over N = 24/48/96) while the single-lattice deviation falls at N^{-2}: the leading lattice artifact is itself S-covariant and CANCELS in the S-relation. T EXACT [E]: T is the discrete Dehn twist -- the Z6 sector map (g,h) -> (g, g+h) x (-1)^F at machine precision (3.6e-13); continuum T-phases not resolvable in the real-positive trace convention (honest scope). CHARACTERS [E]: h_sigma = 1/36 (rel 5.6e-4), parafermionic 1/6 gap (multiplicity 2), omega^{k q} charge weights. SPIN STRUCTURE [E]: deck^3 = (-1)^F closes exactly as Z6 trace arithmetic (1.4e-13) incl. the cover factorization; positive bookkeeping = Z6 charge projection, ground class c = 0 in every sector. TYPED [C]: chiral phases, continuum T-phases, assembly (-> v651), continuum OS; GATE.QGEO does not move.
Original classification detail
ORB-MODULAR-COHERENT: nine sectors match |theta/eta|^2 at < 1%, S measured with a clean N^{-4} rate (the N^{-2} artifact is itself S-covariant and cancels), T exact as the Z6 Dehn shift, h_sigma = 1/36 with the 1/6 gap, deck^3 = -1 exact as Z6 trace arithmetic; chiral phases/continuum OS typed open; GATE.QGEO does not move.
Dependencies as recorded
QGEO.TWISTOPE.01; QGEO.KLEINRP.01; QGEO.ORBCAS.01; v622; v623; v628; v639; v645
Open the original ledger source, row 653Location recorded in the ledger
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- E8 audit and bootstrap
Sections that explicitly cite this claim
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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
Navigation through a shared verification script
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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
- v650_orbifold_modular.pyRegistered verification module · core
Read the description recorded in the module registry
QGEO.ORBMOD.01: die Modular-Daten des ℤ₃-Orbifolds der Naht auf dem Gitter — **ALLE NEUN Z[g,h] TREFFEN |θ[g/3,h/3]/η|² AUF < 1 %, DIE MODULARE S-KOVARIANZ IST GEMESSEN MIT SAUBERER N⁻⁴-RATE (das N⁻²-Gitterartefakt ist selbst S-kovariant und KÜRZT SICH), T IST DER EXAKTE ℤ₆-DEHN-TWIST (g,h) → (g, g+h) × (−1)^F auf Maschinenpräzision** — die getwisteten Charaktere tragen h_σ = 1/36 (rel 5.6e−4) mit dem parafermionischen 1/6-Gap, die v628-Casimir-Tafel reproduziert pro Deck-Klasse, und **deck³ = (−1)^F schließt EXAKT als ℤ₆-Spur-Arithmetik** (inkl. Cover-Faktorisierung; positive Buchführung = ℤ₆-Ladungsprojektion, Grundklasse c = 0 in jedem Sektor); chirale Phasen/Kontinuums-T/OS getypt offen, GATE.QGEO bewegt sich nicht (17 checks, ~25 s)
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