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Original ledger classification: Numerical (exact rep theory) [E]/[O]

Recorded statement: SPECTRAL-ACTION MATTER CONTENT (2026-06-17): the computable core of CONTRACT.QFT4D.01 (v244) -- the NCG matter representation, discharging the representation-theory + tree-relation core to [E] and leaving only the seam->Dirac realisation…

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QFT4D.MATTER.01

Original ledger classification: Numerical (exact rep theory) [E]/[O]

Original claim text

SPECTRAL-ACTION MATTER CONTENT (2026-06-17): the computable core of CONTRACT.QFT4D.01 (v244) -- the NCG matter representation, discharging the representation-theory + tree-relation core to [E] and leaving only the seam->Dirac realisation and the measured-coupling reproduction as the open residual. The carrier half-spinor is the SO(10) 16 (dim S^+ = 2^(g_car-1) = 16). One generation = SO(10) 16 = SU(5)(10+5bar+1) = SM: Q=(3,2)_{1/6}, u^c=(3bar,1)_{-2/3}, e^c=(1,1)_{1}, L=(1,2)_{-1/2}, d^c=(3bar,1)_{1/3}, nu^c=(1,1)_{0}. (1) [E] 16 = one generation: SM multiplet dims sum to 6+3+1+2+3+1 = 16 = dim S^+, N_fam=3 (15 SM Weyl fermions + a right-handed neutrino). (2) [E] electric charges Q=T3+Y are exactly the SM values (quarks +2/3,-1/3; anti-quarks -2/3,+1/3; leptons 0,-1; e^c +1; nu^c 0) -- the hypercharges are forced by the SO(10) embedding. (3) [E] anomaly-free: all four gauge anomalies cancel exactly over the 16: sum Y = 0, sum Y^3 = 0, [SU(2)]^2 U(1) = 0, [SU(3)]^2 U(1) = 0. (4) [E] spectral-action unification: sin^2 th_W = (sum T3^2)/(sum Q^2) = 3/8 at the spectral scale, i.e. g3=g2=sqrt(5/3)g1 (Chamseddine-Connes-Marcolli). (5) [E] Higgs = the (1,2)_{1/2} off-diagonal part of the finite Dirac operator (inner fluctuation), one SM doublet. (6) [O] residual: (i) the seam induces the Dirac operator D and (iii) the spectral action reproduces the MEASURED couplings after RG running -- still a contract, now with its rep-theory core verified

Original classification detail

[E] SO(10) 16 = one anomaly-free SM generation with correct hypercharges/charges; sin^2 th_W = 3/8 (g3=g2=sqrt(5/3)g1); Higgs = (1,2)_{1/2} inner fluctuation. [O] the seam->Dirac realisation + measured-coupling reproduction stay the open contract

Dependencies as recorded

CONTRACT.QFT4D.01; FORM.P2.02

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  • v245_spectral_matter_content.pyRegistered verification module · registry
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    QFT4D.MATTER.01 — the computable core of CONTRACT.QFT4D.01 (v244): the spectral-action / NCG matter content, discharging the rep-theory + tree-relation core to [E]. The carrier half-spinor is the SO(10) 16. [E] 16 = one generation: SO(10) 16 = SU(5)(10+5bar+1); SM dims 6+3+1+2+3+1 = 16 = dim S⁺, N_fam=3 (15 Weyl fermions + ν_R). [E] electric charges Q=T3+Y are exactly the SM values — hypercharges forced by the embedding. [E] anomaly-free: ΣY=0, ΣY³=0, [SU(2)]²U(1)=0, [SU(3)]²U(1)=0 (exact). [E] spectral-action unification: sin²θ_W=(ΣT3²)/(ΣQ²)=3/8, i.e. g3=g2=√(5/3)g1 (Chamseddine–Connes–Marcolli). [E] Higgs = the (1,2)_{1/2} inner fluctuation of the finite Dirac operator (one doublet). [O] residual: the seam→Dirac realisation + measured-coupling reproduction stay the open contract.

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