3203 — The One-Way Tail Cannot Be a Positive Skew-Adjoint Quotient
Adding the adjoint mate produces a positive skew-adjoint block but changes the constant-channel equation. No finite positive skew-adjoint extension can recover the original nonzero nilpotent tail generator as an operator quotient: an invariant quotient of a finite-dimensional skew-adjoint operator is again diagonalizable and skew-adjoint, whereas the triangular tail incidence is nonzero nilpotent.
The mate cell must therefore live in a relative, unbounded, indefinite, or derived construction whose recovery notion is not an ordinary operator quotient.
Durable verification
- Research packet: research/grothendieck/the-one-way-tail-cannot-be-a-positive-skew-adjoint-quotient.md
- Exact checker: research/grothendieck/checkers/check_triangular_tail_not_skew_quotient.py
- Sequence claim: seqclaim-a206bc513dc6e76262893e9a
- Graph event: ev-000000006678-12e8c513-fb69-4391-a73f-81c03ba8b97b