Jordan Spectral Action and the Chirality Problem Q9B in the TTOE Framework — From the Heat Kernel Identification to the Exceptional Jordan Algebra

A systematic exploration (tests T5–T20) of the Jordan spectral action as a route to the chirality problem Q9B: why the universe selects (27, 3) of E6 × SU(3) rather than its conjugate. The TTOE heat kernel expansion is identified with the Chamseddine–Connes spectral action (TTOE = the case of trivial finite geometry). The associativity obstruction of the original Connes framework is shown to be non-intrinsic: the published Jordan extension (Besnard–Farnsworth 2022) admits the exceptional Jordan algebra J3(O) — exactly the 27 of E6 = Str(J3(O_C)) — as coordinate algebra, and E6/J3(O) turns out to be the unique cascade level with both unique Z2 grading (Schur, 27 irreducible) and admissible algebra: chirality becomes a prediction rather than a choice. The Peirce decomposition yields 1+10+16 = 27 with SO(10) emerging as the stabilizer of the idempotent, a natural boson/fermion Z2, the SM Higgs doublet from J0 = 10 with correct charges, and three generations from SO(8) triality — with w0-breaking = triality breaking producing hierarchy, CKM (Wolfenstein), and CP violation from one spurion ε = 0.226. Baez's 2026 theorem (with F4 transitivity) supplies the exact SM gauge group S(U(2)×U(3)) from h3(O). A systematic search across 11 fronts finds no Jordan no-go theorem (a verification, not a proof, as stated). One simple mass-ratio prediction is honestly reported as falsified (factors 5–17000×). Of the 14 layers of Q9B, 12 are resolved or derived and 2 remain conditional; the remaining gaps (explicit Yukawa values, formal no-go proof) are technical.