Proposition: Calibration and geometric nonuniqueness

At a fixed event $e$, exact event calibration

with distinct labels forces one deterministic outcome, or admits no normalized input if $T(e)$ is not a label.

The abstract instrument does not uniquely determine its history times, rod frame, or the global conical deficit.

Proof. Distinctness permits at most one supported index, and total probability is one. If $p_s=1$, positivity implies support in $P_s\otimes I_X$.

For nonuniqueness, retain every finite matrix and reassign the history labels, or rotate and translate the local rod frame with corresponding port coordinates. Different prescribed deficits also admit isometric small regular laboratories carrying the same finite instrument. The finite record law is unchanged.