The closed observation problem

Destructive measurement, a coherent record carrier, and a measurement instrument with a surviving quantum output are different interfaces. A geometric extension of a quantum language must say which of these interfaces it can observe. Linear ownership of quantum names alone does not answer that question.

We take destructive computational-basis readout as a given primitive, with type

Its measured quantum interface is consumed. We use its Born semantics, as in the corresponding finite circuit fragment of the Enter calculus Cheung2026Enter. No characterization or uniqueness proof for the measurement law is repeated here.

The semantic additions are fixed throughout: an external classical geometric configuration, locations for active names, declared coupling algebras, and an explicit control and resource interface. The question is then precise:

Which spectator extensions, deferred implementations, and scale/readout comparisons preserve the outputs that the interface declares accessible?

Our answers concern equality of observable outputs, not a mechanism that constructs geometry from quantum syntax.