The fermionic matter sub-programme of the Cosmochrony corpus addresses a single central question: where do fermions, chirality, hypercharge, and three generations come from? The answer is that they are not postulated as external fields: they arise as the spinorial face of the admissible Weil module V_, once its metaplectic Lie-algebraic structure is complexified by the Lorentzian metric established in the geometric branch. The structural chain is: \ Fₙ V_ Mp (2, R) mp (2, R) C sl₂ (C) Spin (3, 1) SL (2, C) S_. \ Three modular structural results are established in Q14: (A) the admissible spinor bundle S_ reproduces the SU (2) L U (1) Y electroweak bundle structure from tensor functors of S_; (B) the projected Dirac operator D, ₆, ₀ contains a canonical projective endomorphism E_ that enforces the V-A chiral structure (established via the spinorial BI lift theorem of Q14) and whose ₅-weighted a₄ coefficient imposes anomaly-cancellation constraints making hypercharge a spectral datum; (C) the saturation invariant c (n₃) = 3 has a spinorial multiplicity reading yielding a gauge-singlet three-generation factor C³₆₄₍. The colour-coupled quark sector is unconditional at the pointwise level (H-color₎₈₍ₓₖ₈ₒ₄ established in O31). The structural form of E_ is now fixed as a Schur complement of the eliminated spinorial block, and the generation-split amplitude mechanism is derived as Born–Infeld saturation in the companion note ; the open deliverables are its explicit Lorentzian block and the Yukawa sector, while the split value itself is dictionary-bound, its first-principles derivation relocated upstream to the ADE case selection and the cascade exponent.
Jérôme Beau (Sun,) studied this question.