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A registered result in its source context

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

Recorded statement: FIRST-ORDER CONDITION VIOLATED BY THE MAJORANA/sigma (2026-06-17): the Chamseddine-Connes-van Suijlekom 'beyond first order' mechanism exhibited on a faithful minimal model -- advances CONTRACT.QFT4D.DIRAC.01 (v250) from a contract to an…

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Paper context: Research contracts

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PS.DIRAC.01

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

Original claim text

FIRST-ORDER CONDITION VIOLATED BY THE MAJORANA/sigma (2026-06-17): the Chamseddine-Connes-van Suijlekom 'beyond first order' mechanism exhibited on a faithful minimal model -- advances CONTRACT.QFT4D.DIRAC.01 (v250) from a contract to an exhibited mechanism. HONEST CORRECTION to the external review: the sigma field does NOT 'rescue' the first-order condition; the opposite is true (CCvS 2013) -- one DROPS the first-order condition, and the inner fluctuations of D THEN generate the fields that promote the SM gauge group to Pati-Salam SU(2)xSU(2)xSU(4) plus a singlet sigma (which gives the nu_R Majorana mass and drives the breaking). Model: H = H_F (+) H_F^c, H_F=C^3 (nu_L,nu_R,e_R); pi(a)=diag(rho(a),0) on particles; J = swap.conj so J pi(b) J^-1 = diag(0,conj rho(b)); D=[[D_p,M],[M^dag,conj D_p]] with D_p the Yukawa block and M the Majorana (nu_R nu_R^c = sigma) block. (1) [E] order-zero [pi(a),J pi(b) J^-1]=0. (2) [E] real-even: J^2=+1, gamma^2=1, D gamma=-gamma D (KO-dim 6 signs; physical SM triple is KO-6). (3) [E] first order HOLDS for the Yukawa block (M=0): [[D,pi(a)],J pi(b) J^-1]=0. (4) [E] first order VIOLATED with M!=0, supported EXACTLY on the off-diagonal (nu_R nu_R^c) Majorana blocks -- the sigma is the unique first-order violator; the controlled violation IS the Pati-Salam mechanism. (5) [C] sigma=scalaron (M_PS=kappa M_s, v249); physical identification [O] (scalaron<->nu_R nu_R coupling to be proven). (6) [O] the full 96-dim SM/PS finite triple + spectral-action expansion remain the open contract (v250).

Original classification detail

[E] order-zero + real-even (J^2=1,KO-6 signs,D odd) + first order holds(Yukawa)/violated(Majorana, localized to sigma); the CCvS beyond-first-order Pati-Salam mechanism exhibited; [C] sigma=scalaron; [O] full 96-dim triple + spectral action

Dependencies as recorded

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

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Registered verification modules

  • v251_first_order_sigma.pyRegistered verification module · registry
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    PS.DIRAC.01 — the first-order condition is violated EXACTLY by the Majorana/σ term (Chamseddine–Connes–van Suijlekom 'beyond first order' → Pati-Salam + σ), exhibited on a faithful lepton-block model; advances v250 from contract to mechanism. Honest correction: σ does NOT 'rescue' first order — one DROPS it and the inner fluctuations generate PS + σ. [E] order-zero; [E] real-even (J²=+1, γ²=1, Dγ=−γD, KO-6 signs); [E] first order HOLDS for the Yukawa block; [E] first order VIOLATED by M≠0, supported exactly on the ν_R ν_R^c blocks (σ the unique violator) — the controlled violation IS the PS mechanism. [C] σ=scalaron (v249). [O] the full 96-dim SM/PS triple + spectral action (v250).

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