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many thanks for instructions. Before I deleve into full details, please let me emphasize my point again, while having your Am. J. Phys. 79 (2011) 954. arXiv:1007.4281 in mind.
Any set of consistent histories as per eq. (16) may not be consistent for some alternative TPS. For the sake of illustration, let me refer to the hydrogen atom’s structures: ‘electron+proton (e+p)’ and ‘center-of-mass+relative (internal, CM+R)’. Now, considering eq.(16) for the e+p structure does not define a history for the CM+R structure, and vice versa. This simple mathematical fact originating from Entanglement Relativity is my true concern, which does not reduce to the choice of the set of consistent histories you’re mentioning above*. Rather, once made a choice for the e+p excludes the possibility of making a choice for the CM+R atomic structure.
*As long as the TPSs are not regarded [e.g. in eq.(4)] or the TPS is fixed [as assumed in your answer to my previous question], my objection is irrelevant.
Looking forward for further instructions,