TFPT scientific source excerpt
Original repository path: verification/v250_dirac_triple_contract.py
Original file SHA-256: ab2fb45997bc3b8b7dd32e66c52c315c1bbdac7df43d0bd7d3ccfe16ba94d089
Inclusive original lines: 1-28
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000001 | """v250 -- CONTRACT.QFT4D.DIRAC.01: the spectral-triple contract that would turn
000002 | [OMITTED: non-scientific conversation or execution metadata]
000003 | sigma=scalaron).  This module TYPES the obligations honestly and checks the finite
000004 | facts; it does NOT construct the operator or close the NCG axioms.
000005 | 
000006 | The target object is a real, even, almost-commutative spectral triple
000007 |     (A, H, D, J, gamma) = (C^inf(M) (x) A_F,  L^2(M,S) (x) H_F,
000008 |                            D_M (x) 1 + gamma_5 (x) D_F,  J, gamma)
000009 | with A_F the Pati-Salam algebra (v248), H_F = 3 x 16, and D_F built from the TFPT
000010 | flavor data (R, L, phi0, Majorana branch).
000011 | 
000012 |   [E] 1. FINITE HILBERT SPACE.  H_F = N_fam x dim S^+ = 3 x 16 = 48 (three
000013 |         generations of the SO(10) spinor); the PS algebra A_F (v248) acts on it.
000014 |   [E] 2. THE YUKAWAS ARE NOT THE TEST.  The charged-fermion mass ratios are ALREADY
000015 |         fixed by the TFPT flavor layer (FLAV.QUARK.01 / v18: mt/mb=40.8, etc.), so
000016 |         D_F's textbook output is in place -- the OPEN test is NCG CONSISTENCY of
000017 | [OMITTED: non-scientific conversation or execution metadata]
000018 |   [O] 3. THE NCG OBLIGATIONS (the contract).  For the explicit D_F one must verify,
000019 |         exactly: reality J (J^2 = +/-1), grading gamma, KO-DIMENSION (6 mod 8),
000020 |         the FIRST-ORDER CONDITION [[D,a],Jb*J^-1]=0 (the historic SO(10)-NCG
000021 |         obstruction), orientability, Poincare duality, and NO-JUNK (the quotient by
000022 |         junk forms).  None is closed here.
000023 |   [O] 4. sigma = SCALARON HYPOTHESIS.  Chamseddine-Connes-Mukhanov rescue the
000024 |         first-order condition with a singlet scalar sigma that also generates the
000025 |         nu_R Majorana mass.  Conjecture (supported by M_PS = kappa M_s, v249): this
000026 |         sigma IS the R+R^2 scalaron.  CAVEAT [honest]: the scalaron's coupling to
000027 |         nu_R nu_R (Majorana) is NOT automatic -- the identification (matching
000028 |         quantum numbers + couplings) must be PROVEN, not assumed.