The Neutrino Sector from Spin(8) Triality on K_7 / K_8: Three Generations, Three Sterile Partners, delta_CP and the PMNS Matrix from a Single Substrate-Based Recipe

Paper 19 of the Null Worldtube Theory (NWT) program closed the gravitational-Standard-Model column through a single library, nwt_substrate. The present paper turns that machinery on the neutrino sector and produces three sharp predictions from the substrate algebra alone: (i) a concrete three-mass sterile-neutrino spectrum in the 60-220 MeV nu-MSM window with universal active-sterile mixing |U_alpha 4|^2 ~ 2.4 x 10^-10; (ii) the Dirac CP phase |delta_CP| = 2 pi / 3 = 120 degrees as a Z_3-winding magnitude with sign -2 pi / 3 under the Baez Fano octonion-product convention; (iii) the leading-order PMNS angles theta_12 = arctan(1/sqrt 2), theta_23 = pi / 4, theta_13 = arcsin sqrt(3 alpha) from Spin(8) triality. These three predictions, together with the K_8 active-neutrino mass formula inherited from Paper 19, follow from edge-counting on the complete graphs K_7 and K_8 with structural integers shared across Papers 17-19. The recipe is edge-counting on K_7 and K_8 under the action of the natural cyclic automorphism Z_3 subset of G_2 = Aut(O). Five layers of structure feed into the predictions: the combinatorial K_7 = 21 edge decomposition 6 + 3 + 12 under Z_3 matches the substrate-boson partition introduced in Paper 19; the representation theory of G_2 to SU(3) via the S^6 stabilizer organizes the neutrino sector into 1 + 3 + 3-bar with active flavors in the 3 and three sterile partners in the 3-bar; the orbit-resolved seesaw ratio m_active / m_sterile = alpha^(9/2) ~ 2.4 x 10^-10 follows from the assignment and the 12 vs 3 SM-flavor vs internal-SU(2) edge split; combining with Paper 19's K_8 phase-soliton mass formula yields the unified Wilson ansatz m = (8 / N_v) alpha^(N_e / 2) (1 + alpha/7) (1 + 3 alpha^2) m_Pl with (N_v, N_e) = (7, 21) for the electron, (8, 28) for each active neutrino, and (8, 19) = (8, 28 - 9) for each sterile partner; the K_8 extension is structurally forced because the Spin(7) subset of Spin(8) embedding stabilizes a unit vector in V_8 (Baez 2002), and identifying this with the eighth K_8 vertex decomposes the 28 edges as 6 + 3 + 12 + 1 + 6 (Lorentz + internal SU(2) + SM-flavor + Higgs vacuum + Yukawa). Predictions: active neutrino masses m_1 = 14.84 meV (first-principles from Paper 19 W3.3-J), m_2 = 17.16 meV, m_3 = 53.00 meV with Sum m_nu = 85 meV; sterile masses m_N1 = 61.3 MeV, m_N2 = 70.8 MeV, m_N3 = 218.8 MeV in the nu-MSM mass window targeted by SHiP, PIONEER, NA62, and DUNE-near; active-sterile mixing |U_alpha 4|^2 ~ alpha^(9/2) ~ 2.4 x 10^-10 at the edge of current bounds; PMNS angles at leading order tri-bi-maximal with theta_13 = arcsin sqrt(3 alpha); Dirac CP phase |delta_CP| = 2 pi / 3 in magnitude with sign -2 pi / 3 in the Baez Fano convention (~0.2 sigma agreement with T2K-only, ~2.6 sigma tension with NuFIT 6.0 global fit, to be resolved by DUNE and Hyper-K); Jarlskog invariant |J_CP| = 0.029. Falsifiers: hard exclusion of all three sterile masses in 50-250 MeV at |U_alpha 4|^2 >= 10^-11 falsifies the triality seesaw; a future global-fit measurement settling |delta_CP| outside [110, 130] degrees at > 3 sigma falsifies the Z_3-winding magnitude prediction; detection of any fourth-generation active neutrino or a non-normal hierarchy falsifies the K_8 identification. A companion strand of the program (forthcoming Paper 22) treats the cosmogenic origin of our universe within the same substrate framework; the polar vertex of the cosmogenic K_7 embedding aligns with the parent black hole's spin axis (identified in companion work with the CMB Axis of Evil), the three equatorial bridging edges yield the azimuthal l=3 Maxwell-vector pattern in the AoE-perpendicular plane, and the K_8 active-mass formula couples to a non-trivial dark sector whose joint signature with Sum m_nu is also discussed. Where the present analysis depends on this cosmogenic framing, the dependence is flagged explicitly. Reproducibility: the analysis scripts that reproduce the three-generations derivation, the G_2 to SU(3) stabilizer calculation, the K_8 active-mass formula and sterile-neutrino mass predictions, the Wilson-amplitude construction of the PMNS matrix, and the gauge-invariance checks are available at https://github.com/JimGalasyn/null-worldtube. The substrate-algebraic computation library that underlies the K_7, so(7), Spin(7), and Cl(0,7) identities used throughout (with import-time-asserted structural constants, K_8 extension as nwt_substrate.neutrino, and 606 cross-shim tests including 31 K_8 neutrino-sector tests) is at https://github.com/JimGalasyn/nwt-substrate (concept DOI 10.5281/zenodo.20041585).