Manipulations and non-identifications

Thus the statement “the fourth dimension is the factor Enter consumes” is used, at most, as an operational analogy. Literally, the geometric time coordinate remains present after the finite clock factor is consumed.

Three spatial rod coordinates likewise do not imply that a continuum relativistic field has a tensor factor for each rod or point. The finite name factorization is an independent apparatus choice.

The classical lapse constructions of Em02-E and XX-A, and the separations of XIX-A, retain their own backgrounds, rods, and inverse maps CheungLapse. No comparison map identifies their lapse with the code $k$, the pointer ${\sum }_k{T}_k{P}_k$, or the schedule time.

Record agreement alone is insufficient: identity and computational dephasing have identical one-outcome coarse records, but on $|+⟩⟨+|$ their residuals are $|+⟩⟨+|$ and $I/2$. Their trace distance is $1/2$. The complete instruments, not merely records, are therefore used throughout CheungEn03.

Finally, two distinct conical deficits admit isometric regular laboratories of any fixed finite size. Installing the same analytical packet and finite matrices in those laboratories gives the same local records, although the global conical completions differ. The present records do not determine the deficit.