A registered result in its source context
Original ledger classification: Exact [E] closed forms and expansions (sympy exact; Python-only per GATE.WOLFRAM.02).
Recorded statement: The orbifold Casimir round (one module, 5 checks, ~1 s; discovery probe orbifold_casimir_probe.py 5/5, verdict ORBIFOLD-CASIMIR-EXACT). The covered seam's three deck-mode classes {1/6, 1/2, 5/6} carry EXACTLY the Z3-twist Casimir data:…
Statement, assumptions and sources
Paper context: input 5 tfpt 3 e8 audit bootstrap
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QGEO.ORBCAS.01
Original ledger classification: Exact [E] closed forms and expansions (sympy exact; Python-only per GATE.WOLFRAM.02).
Original claim text
The orbifold Casimir round (one module, 5 checks, ~1 s; discovery probe orbifold_casimir_probe.py 5/5, verdict ORBIFOLD-CASIMIR-EXACT). The covered seam's three deck-mode classes {1/6, 1/2, 5/6} carry EXACTLY the Z3-twist Casimir data: exact closed form E0(nu, N) = -cos(pi(2nu-1)/(2N))/(2 sin(pi/(2N))); finite-size coefficient exactly pi(6nu^2 - 6nu + 1)/12; sector table (1/72, -1/24, 1/72); degenerate twisted pair; ratio -1/3; twist gap 1/18. [2026-08-02 XLI: the named interacting residue executed -- v639: twist-field weights from three exact routes (h_sigma = 1/36), lattice two-point 2 Delta = 2/9 at < 0.11%, crossing exactly symmetry-protected, closed four-point form, OPE data (c1 = 2/9 model-bound); RP validated in the real Z2 class, the complex Z3 pairing (parafermionic Klein twist) typed open; GATE.QGEO does not move; see QGEO.TWISTOPE.01.]
Original classification detail
ORBIFOLD-CASIMIR-EXACT: the kinematic half of the Z3 orbifold statement is exact; the interacting statement (twist-field OPE, crossing, RP) stays the named residue; GATE.QGEO does not move.
Dependencies as recorded
QGEO.COVERSEAM.01; QGEO.SEAMID.01; v622; v623
Open the original ledger source, row 642Location 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
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- Front matter / supportE8 audit and bootstrap
- 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
- v628_orbifold_casimir.pyRegistered verification module · core
Read the description recorded in the module registry
QGEO.ORBCAS.01: die Orbifold-Casimir-Runde — **DIE DREI DECK-MODENKLASSEN DER GEDECKTEN NAHT TRAGEN EXAKT DIE ℤ₃-TWIST-CASIMIR-DATEN** (erste quantitative Scheibe des v623-Orbifold-Rests). [E, exakt] Geschlossene Form E₀(ν,N) = −cos(π(2ν−1)/2N)/(2 sin(π/2N)); 1/N-Koeffizient exakt π(6ν²−6ν+1)/12; Sektor-Tabelle (1/72, −1/24, 1/72) für ν = (1/6, 1/2, 5/6): Twisted-Paar entartet, Verhältnis −1/3, Twist-Gap 1/18 exakt. [C] Der verbleibende Rest ist die WECHSELWIRKENDE Aussage (Twist-Feld-OPE, Crossing, RP) (5 checks, ~1 s)
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