Geometry remains input data

The circumference of $r=R$ is $2\pi \alpha R$. Hence the global deficit is $\mu$. Locally, every sufficiently small regular patch is flat. Neither fact is inferred from a quantum record.

No source map, metric-update rule, or matter action on $(M,g)$ is included in the geometric specification. In particular, the two species of the following algebraic problem do not become two dynamically coupled metrics on $M$.