Proposition: A same-channel geometric countermodel

The complete finite experiment just constructed does not determine the global conical deficit.

Proof. Choose two deficits ${\mu }_1\ne {\mu }_2$. Their regular products each contain a developing patch isometric to the same sufficiently small Euclidean spatial ball times a time interval. Install identical names, matrices, table values, clock calibrations, and target-adapted routes in these two patches.

Every finite channel and record law is identical, since all operations use the same local data. The completed backgrounds nevertheless have different marked circumference-to-radius ratios $2\pi -{\mu }_1$ and $2\pi -{\mu }_2$. Thus the same finite operational data do not determine the global deficit.