Proposition: The complete records do not select the dictionary

The finite recorded channels constructed here do not uniquely determine the rod frame, the lapse, or the global conical deficit.

Proof. Translate or rotate the developing coordinates and all finite carrier locations. The matrices and the complete instruments are unchanged, while the rod numbers change.

For the lapse comparison, retain the same coordinate events and channels but compare $g_1=-c^2\mathrm{d}{T}^2+h$ and $g_2=-4c^2\mathrm{d}{T}^2+h$. Every wire causal for $g_1$ is causal for $g_2$, but a static coordinate interval has different proper durations. The same channel data therefore do not fix the lapse calibration.

Finally, two different deficits admit isometric regular balls. Install the same finite ports and the same flat-completion detector package in such balls. Their complete output channels coincide, although the global circumference-to-radius ratios differ.