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Original ledger classification: Contract [O] (with [E] finite facts)

Recorded statement: THE SPECTRAL-TRIPLE CONTRACT (2026-06-17): the object that would turn 'carrier is gauged' from a fork into a theorem (Reviewer-A Theorem 3 + the sigma=scalaron identification). Target: a real even almost-commutative triple (A,H,D,J,gamma)…

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Paper context: tfpt research contracts

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CONTRACT.QFT4D.DIRAC.01

Original ledger classification: Contract [O] (with [E] finite facts)

Original claim text

THE SPECTRAL-TRIPLE CONTRACT (2026-06-17): the object that would turn 'carrier is gauged' from a fork into a theorem (Reviewer-A Theorem 3 + the sigma=scalaron identification). Target: a real even almost-commutative triple (A,H,D,J,gamma) with A_F = PS algebra (v248), H_F = 3x16, D_F = D_M (x) 1 + gamma_5 (x) D_F(R,L,phi0,Majorana). (1) [E] H_F = N_fam x dim S^+ = 3x16 = 48 (three generations of the SO(10) spinor); A_F acts on it. (2) [E] the charged-fermion Yukawas are ALREADY fixed (FLAV.QUARK.01/v18), so the open test is NCG CONSISTENCY of D_F, not 'nice Yukawas' (Reviewer A). (3) [O] the 7 NCG obligations: reality J, grading gamma, KO-dimension (6 mod 8), the FIRST-ORDER CONDITION (the historic SO(10)-NCG obstruction), orientability, Poincare duality, no-junk forms. (4) [O] sigma=SCALARON HYPOTHESIS: the Chamseddine-Connes-Mukhanov singlet sigma (rescues first-order + gives nu_R Majorana) is conjectured to BE the R+R^2 scalaron (supported by M_PS=kappa M_s, v249); CAVEAT: the scalaron<->nu_R nu_R coupling is NOT automatic and must be proven. (5) [O] inner fluctuations Omega^1_D -> Higgs content 10+16+45 not 126 (NCG complement of v247). (6) [C] verdict: reduces the '4d QFT' residual to ONE constructive object (the triple) + the finite NCG checks; gauge group (v248), matter rep (v245), Yukawas (v18) and unification corridor (v249) already in place -- what is missing is D_F + its axioms.

Original classification detail

[E] H_F=3x16=48, Yukawas already fixed (test is NCG consistency); [O] the 7 NCG axioms (first-order condition the hard one), sigma=scalaron, inner-fluctuation Higgs content -- reduces 4d QFT to one spectral triple

Dependencies as recorded

PS.ALGEBRA.01; CONTRACT.QFT4D.01

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Registered verification modules

  • v250_dirac_triple_contract.pyRegistered verification module · registry
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    CONTRACT.QFT4D.DIRAC.01 — the spectral-triple contract that would make 'carrier gauged' a theorem. Target (A,H,D,J,γ) almost-commutative, A_F = PS (v248), H_F = 3×16, D_F from (R,L,φ0,Majorana). [E] H_F = 3×16 = 48; [E] the Yukawas are already fixed (v18) so the open test is NCG consistency; [O] the 7 NCG axioms (first-order condition the historic SO(10) obstruction); [O] σ=scalaron hypothesis (rescues first-order + ν_R Majorana; M_PS=κM_s) — CAVEAT scalaron↔ν_Rν_R not automatic; [O] inner fluctuations → 10+16+45 not 126 (NCG complement of v247). Reduces 4d QFT to one object + finite NCG checks.

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