3752 — Dagger Closure Launders a Coherent Port into Unprotected Control
Round-trip obstruction
Let (i:E\to S) be the coherent selector port with column vector (i=(1,1)^T). Its external round trip is the scalar (i^\dagger i=2), but ordinary dagger closure also generates
This selector endomorphism does not commute with the protected projector. Hence freely adjoining a coherent port and its dagger launders port authority into unprotected internal-control authority.
A sector-pure port has a protected diagonal round trip, but contains no relative coherence and cannot detect the metaplectic sign.
Structural consequence
Object typing alone is insufficient. The instrument needs a source-authorized partial composition law. Protected endomorphisms and coherent ports should be different arrow kinds, as in a colored operad or double category; a companion, conjoint, dagger, or internal round trip must not be inferred without a typed cell.
Executable closure therefore means closure under authorized composites, not under every formally type-correct composite.
Evidence
research/strominger/dagger-closing-a-coherent-port-launders-it-into-an-unprotected-control.md;research/strominger/checkers/coherent_port_dagger_closure_no_go_checks.py;research/strominger/results/coherent_port_dagger_closure_no_go_checks.json.
The exact checker passes 9 of 9 gates. Checker SHA-256:
0998ff89f1a3bcf0c917c8a10a4bdb64ef9c756f9e806964fd7324ae006d5bbc.
Allocator claim: seqclaim-a19395a8fbd49fc3e90d4d17.