Operator Doublets, Erased History Fibres, and the No-Sequential-Re-entry Theorem

Fermionic-matter sub-programme no-go note.

The note closes, with exact finite proofs and machine certification, the two deposited candidates for the missing fermionic weak-isospin carrier of the Cosmochrony corpus.

Main results

• Abelian carrier commutant: the commutant of the finite Weil module is spanned by the two parity projectors, so no non-abelian connected action commutes with the Weil action on V_c; the canonical Hecke M_2(C) doublets of End(V_c) have no fermionic lift to their own carrier.
• Erased-fibre structure: the symmetric Cayley alphabet has stabiliser exactly C4; the fibre of the canonical projective channel over a b-shadow with r zero-runs is canonically a torsor under the abelian run-flip group (Z2)^r; the canonical inductions of the history space carry only near-regular multiplicities, with no privileged M_2(C) factor.
• Alternating transport and axis exchange: the flip-antisymmetric fibre line maps exactly to the parity-odd operator sector, but the two odd Hermitian axes i(A_X +- A_Y) are exchanged by a semilinear automorphism of the cocycle-enriched Heisenberg--Weil datum, implemented by the deposited antiunitary RK; no natural selector exists, and the coordinate formula that selects one is conditional on an oriented central/Weyl pinning.
• No-sequential-re-entry theorem: the canonical record quotient satisfies pi v = 0 => Q pi v = 0 for every downstream linear Q, and the channel's conditional expectations annihilate the mu-centred fibre differences for every non-degenerate measure; no tower of sequential projections recovers the erased alternating character.
• Architectural dichotomy (history-fibre route): realisation requires a parallel channel from the pre-projection space plus an orientation of (Z, w) --- two new ingredients, or one new axiom supplying both; an independent new carrier outside the deposited corpus remains a distinct, unconstrained extension architecture.

Reproducibility

The three archived scripts in scripts/ certify every computational claim and rerun in about one second in total:

• front_hist_fibre_doubling.py: frame stabiliser (exhaustive at q = 13, 29, 53), fibre bijection and Pell counts (n <= 10), C4 freeness, flip involutions, exact alternating transport at q = 29;
• front_axis_selector.py: enriched-data symmetry table, RK intertwining and RK F RK = F^{-1}, conditional coordinate-pinned selector, single-line support obstruction;
• front_joint_reentry_audit.py: exact rational two-point fibre algebra (uniform and non-uniform conditional expectations, mu-centred kernel line), no-re-entry implication, exhaustive Heisenberg-automorphism check at q = 5.

Status

Unpublished draft (branch 0.1). No release cascade has been triggered.

Compilation

bash compile.sh

Output: out/NoSequentialReentry.pdf.