The characteristics of the precipitating object would have to be sufficiently consistent with the characteristics of the dissolved object if it is to give the appearance of being the same object - consistent, that is, but not necessarily identical (a trivial example would be that the precipitating object will in all likelihood have a different spatial relationship to other objects and thus appear to some of those objects to have moved). Regarding the attributes of the precipitating object, this scenario would permit a range of possible values that could be assigned to certain of those attributes - i.e. values that would all be consistent with it being the same object that had previously “dissolved” - but for which only one value can be actualised (i.e. observed or measured).
(Note that this would be consistent with the stochastic character of the measurements or observations of the kinds of objects studied in quantum physics and which gave rise to the idea of “wave function collapse”, thereby engendering the measurement problem. It should be noted that the scenario outlined above pertains only to objects that are simple enough to undergo periods of non-interaction with any other object, and so would render impotent Schrodinger’s attempt to subject the “Copenhagen Interpretation” of quantum mechanics to a reductio-ad-absurdum by use of his famous “cat-in-a-box” thought-experiment. It may also be pertinent to the “Quantum Zeno Effect”. See appendix 1.)
All hierarchies within the all-in-all can now be seen to resolve downwards (on the pyramid analogy) to a common base-layer comprised of quantum objects. Also, the apex of any hierarchy implicated in a compound object will most likely be a member of a more encompassing hierarchy, and this kind of layering would continue upwards until all such hierarchies converge either upon a single apex associated with the entire all-in-all, or upon a set of such apexes that collectively constitute an aggregate.