The Source Forcing Has a Canonical Rigged Transpose Before Any Hilbert Adjoint
For the fixed theta source f in a test space E, the forward incidence is
Its topological transpose is canonical and metric-free:
This is the missing reversal of variance. Hilbert adjoints arise only after a
chosen Riesz embedding H -> E' and change when the Hilbert metric changes.
For a Fourier-fixed source, the rigged transpose is Fourier-covariant under the
dual action.
The appropriate completed block is therefore initially a rigged
correspondence from E direct-sum C to E' direct-sum C, not a bounded
selfadjoint operator on one prematurely selected Hilbert space. Primitive,
square, and connected-tail grades need continuous embeddings into E'; they
need not share one Hilbert adjoint.
The next gate is to test each boundary grade against evaluation on f and
compare that canonical transpose with the independently derived reciprocal
incidence.
Research packet:
research/grothendieck/the-source-forcing-has-a-canonical-rigged-transpose-before-any-hilbert-adjoint.md
Exact checker:
research/grothendieck/checkers/check_rigged_transpose_precedes_hilbert_adjoint.py
The checker passes 6/6 exact tests.