Abstract

We separate three obligations that cannot be discharged by renaming a finite quantum circuit: deriving a channel from a specified generator, acquiring an unknown source through a complete instrument, and identifying the acquired parameter with a physical source observable. On a two-vertex graph we construct a finite synthetic source model with an opposite-sign kick, finite random-kick nuisance, and a collision-induced relaxation surrogate. Its channel and destructive Enter instrument are derived explicitly, including arbitrary untouched references. The likelihood depends on two kick moments. We prove calibrated finite-shot estimation, complete-record model compatibility, and discrimination certificates for predeclared competing families. An explicit equal-record example shows that different source weights can become indistinguishable when the nuisance is allowed to vary.

A separate conditional theorem transfers these results to a physical source observable when a source encoding, a microscopically derived acquisition instrument, and certified comparison allowances are supplied. Those physical matching data are not present in the supplied materials. Consequently the finite-model and conditional results are proved, but the unconditional physical positron acquisition-and-identification theorem remains unconstructed. No continuum transport law, Galactic 511\,keV morphology or rate, thermodynamic reset cost, or spacetime embedding is inferred.