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Spec 1.7 F.3.1 contains
This suggests to me that shared objects are objects shared between pages rather than objects shared between a page and another non-page object. This interpretation results in objects that are reachable from a low priority object and a higher priority object are promoted to the higher priority part rather than demoted to the lower priority part, which intuitively seems to make sense.
This suggests to me that the tests to determine allocation to parts should be as given here.
(Some tests suppressed.)