The finite projective corpus contains two natural candidates for the missing fermionic weak-isospin carrier: the canonical multiplicity-two Hecke doublets of the internal operator algebra End (V₂), and the exponentially rich fibre of history data erased by the canonical projective channel. This note proves that neither candidate, nor any sequential combination of the deposited structures, produces that carrier at the current stratum. Four exact obstructions are established. First, the commutant of the finite Weil module is spanned by the two parity projectors, so every connected unitary action commuting with the Weil action on V₂ is abelian: the operator doublets admit no fermionic lift to their own carrier. Second, the erased history fibres are structurally abelian: the symmetric Cayley frame has stabiliser exactly C₄, the fibre over a b-shadow with r zero-runs is canonically a torsor under the abelian run-flip group (Z₂) ʳ, and every canonical induction of the history space yields only near-regular multiplicities with no privileged M₂ (C) factor. Third, the flip-antisymmetric fibre line does transport to the parity-odd operator sector, but the two resulting Hermitian axes i (AₗAₘ) are exchanged by a semilinear automorphism of the cocycle-enriched Heisenberg–Weil datum, implemented by the deposited antiunitary RK; no deposited datum selects one axis, and the coordinate formula that does is conditional on an oriented central/Weyl pinning that is itself an additional datum. Fourth, and centrally: the canonical record quotient annihilates every intra-fibre difference and satisfies v=0 Q v=0 for every downstream linear map Q; the amplitude-level conditional expectations of the channel annihilate the correspondingly -centred vectors for every non-degenerate measure, so no tower of sequential projections or subsequent linear processing can recover the alternating fibre character erased at the first stratum. The corollary is an architectural dichotomy for the history-fibre route: realising the history-derived odd operator requires a parallel channel from the pre-projection space together with an independent orientation of the central and Weyl generators — two new ingredients, or one new axiom supplying both; either way an extension architecture rather than a derivation of the deposited corpus. Interpretive status. All computational claims are machine-certified by three archived scripts; mathematical statements are proved here or imported with explicit citations. The note closes the two deposited candidate routes; it does not exclude an explicitly axiomatised parallel channel, nor an independent new multiplicity carrier outside the deposited corpus, and it leaves the fermionic multiplicity target itself untouched and open.
Jérôme Beau (Wed,) studied this question.