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A registered result in its source context

Original ledger classification: Numerical (NCG axioms) [E]/[C]/[O]

Recorded statement: FULL 96-DIM FINITE SPECTRAL TRIPLE BUILT + NCG AXIOMS VERIFIED (2026-06-17): advances CONTRACT.QFT4D.DIRAC.01 (v250) from a contract listing 7 open obligations to a concrete object on which 5 are discharged to [E]. H_F = H_particle (+)…

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Paper context: Research contracts

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PS.DIRAC.02

Original ledger classification: Numerical (NCG axioms) [E]/[C]/[O]

Original claim text

FULL 96-DIM FINITE SPECTRAL TRIPLE BUILT + NCG AXIOMS VERIFIED (2026-06-17): advances CONTRACT.QFT4D.DIRAC.01 (v250) from a contract listing 7 open obligations to a concrete object on which 5 are discharged to [E]. H_F = H_particle (+) H_antiparticle = particle/antiparticle doubling of three SO(10) 16-plets, dim 96 = 2 x Omega_adm. One generation = nu_L,nu_R,e_L,e_R (colour singlets) + (u,d)x(L,R)x3 colours = 16. D_F = [[S,T],[T^dag,conj S]] with S the Dirac/Yukawa block and T the Majorana (nu_R nu_R^c = sigma). J = (particle<->antiparticle swap).conj; gamma = chirality (flipped on antiparticles). A_F = C(+)H(+)M_3(C) as a bimodule: particles via (lambda,q) colour-trivial, antiparticles via (lambda,m) weak-trivial. (1) [E] dim 96. (2) [E] D_F=D_F^dag and D_F gamma=-gamma D_F. (3) [E] reality J^2=+1, JD=DJ. (4) [E] gamma^2=1, [gamma,pi(a)]=0, J gamma=-gamma J. (5) [E] KO-dimension 6 mod 8 (Chamseddine-Connes-Marcolli). (6) [E] order-zero [pi(a),J pi(b) J^-1]=0 for the SM algebra. (7) [E] first-order condition HOLDS for the SM algebra C(+)H(+)M_3 INCLUDING the full Majorana term (van Suijlekom). (8) [E] first-order VIOLATED for the Pati-Salam algebra (an SU(2)_R pairing nu_R with e_R) EXACTLY by the Majorana, with the violation supported exactly on the right-handed lepton doublet {nu_R,e_R} -- the Chamseddine-Connes-van Suijlekom beyond-first-order mechanism (SM -> Pati-Salam + sigma, cf v251) now on the full 96-dim triple. (9) [E] eigenvalues of D_F reproduce the fermion spectrum: charged Dirac eigenvalues = +/- m_f (all 9 charged masses) and the neutrino block gives the type-I seesaw m_light = m_D^2/M_R. (10) [C] Poincare duality: the intersection (multiplicity) form is non-degenerate (det!=0). (11) [O] orientability (Hochschild cycle), no-junk 1-forms and the spectral-action heat-kernel expansion remain open.

Original classification detail

[E] dim 96 + Hermitian/odd + reality J + grading + KO-6 + order-zero + first-order holds(SM)/violated(PS, localized to nu_R,e_R) + spectrum=masses+seesaw; [C] Poincare duality; [O] orientability + no-junk + spectral action; discharges 5 of the 7 v250 obligations to [E]

Dependencies as recorded

CONTRACT.QFT4D.DIRAC.01; PS.DIRAC.01; PS.ALGEBRA.01

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Registered verification modules

  • v252_full_finite_triple.pyRegistered verification module · registry
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    PS.DIRAC.02 — the FULL 96-dim finite spectral triple (A_F,H_F,D_F,J,γ) built explicitly with NCG axioms verified; advances v250 from a 7-obligation contract to a concrete object discharging 5 to [E]. H_F = particle⊕antiparticle doubling of three SO(10) 16-plets (dim 96). [E] dim 96; D_F Hermitian+odd; reality J²=+1,JD=DJ; grading γ²=1,[γ,a]=0,Jγ=−γJ; KO-dim 6; order-zero; first order HOLDS for SM C⊕H⊕M₃ (incl. Majorana) and VIOLATED for Pati-Salam exactly by the Majorana on {ν_R,e_R} (CCvS beyond-first-order → PS+σ); spectrum = fermion masses + seesaw m_light=m_D²/M_R. [C] Poincaré duality (intersection form non-degenerate). [O] orientability + no-junk + spectral-action expansion.

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