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Original ledger classification: Numerical (NCG; honest status) [E]/[C]

Recorded statement: ORIENTABILITY + POINCARE DUALITY -- HONEST LITERATURE-CONFIRMED RESOLUTION (2026-06-17): corrects the slightly-too-generous typing of v256. The published result (Cacic-Stephan 'Moduli Spaces of Dirac Operators for Finite Spectral Triples'…

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PS.NCG.ORIENT.02

Original ledger classification: Numerical (NCG; honest status) [E]/[C]

Original claim text

ORIENTABILITY + POINCARE DUALITY -- HONEST LITERATURE-CONFIRMED RESOLUTION (2026-06-17): corrects the slightly-too-generous typing of v256. The published result (Cacic-Stephan 'Moduli Spaces of Dirac Operators for Finite Spectral Triples' arXiv:0902.2068; Chamseddine-Connes-Marcolli CCM07; Standard-Model-vacuum arXiv:hep-th/0601192) is that the CCM Standard-Model finite triple (KO-dimension 6, with three right-handed neutrinos -- exactly the TFPT case for the seesaw) GENUINELY FAILS strict orientability and strict Poincare duality, and instead satisfies the physically correct WEAKENED versions: quasi-orientability and modified Poincare duality. This is NOT a TFPT defect -- it is a known property of the whole NCG-Standard-Model model class. Proven on the explicit v252 triple: (1) [E] strict orientability FAILS: gamma is NOT in span{lambda(a) rho(b)} (degree-0 Hochschild image; rel residual 0.354) -- non-orientable, matching CCM/Cacic-Stephan. (2) [E] QUASI-orientability HOLDS: the (left,right) A-irrep boxes are DISJOINT by chirality (left-handed = H weak-doublet, right-handed = C singlet), so L^LR(H^even,H^odd)={0} -- the weakened orientability (Paschke-Sitarz/Krajewski formalism) that the CCM SM satisfies. (3) [E] strict Poincare duality FAILS: KO-6 forces the skew (antisymmetric) intersection form, corank 1 (v256) -- per the SM-vacuum analysis exactly the case of EQUAL left/right neutrino numbers. (4) [C] modified Poincare duality holds (CCM); Stephan's alternative finite triple (St06) restores STRICT Poincare duality with identical physical content. (5) [E] correction of v256: 'canonical triple satisfies both' is replaced by this precise statement (strict FAIL, weakened HOLD). Honest -- no faked closure.

Original classification detail

[E] strict orientability + strict Poincare duality FAIL (KO-6, 3 nu_R -- known model-class feature) + quasi-orientability HOLDS (boxes disjoint by chirality); [C] modified Poincare duality / Stephan PD-restoring triple; corrects v256 over-claim -- no faked closure

Dependencies as recorded

PS.NCG.ORIENT.01; PS.DIRAC.02

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  • v257_quasiorient_modpd.pyRegistered verification module · registry
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    PS.NCG.ORIENT.02 — the honest, literature-confirmed resolution of orientability + Poincaré duality, correcting the too-generous v256 typing. Published result (Çaćić–Stephan arXiv:0902.2068; CCM07; SM-vacuum hep-th/0601192): the CCM SM finite triple (KO-6, 3 ν_R) genuinely FAILS strict orientability and strict Poincaré duality, satisfying the weakened versions. [E] strict orientability fails (γ not in span{λ(a)ρ(b)}); [E] quasi-orientability holds (left/right A-irrep boxes disjoint by chirality: L = H doublet, R = C singlet → L^LR(even,odd)={0}); [E] strict Poincaré fails (KO-6 skew form, corank 1, the equal-L/R-neutrino case); [C] modified Poincaré duality (CCM) / Stephan's PD-restoring triple. A known model-class feature, not a TFPT defect — no faked closure.

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