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I suspect that you will see page authority benefit on each page but that domain authority will be relatively unchanged.  But I don't think that is because of the IP address.   I think the fact that site A Pages 1 and 2 are on the same domain will be the bigger factor.  If you had a shared hosting solution with multiple domains that had significant domain authority (and who doesn't right?) I think you could get benefit from linking from each domain.

Interestingly, I just put the same test in the field about 8 hours ago.  I'll share my results with you as well.

I wonder if the IP matters at all.  I have read "warnings" about being careful of shared hosting solutions due to the possibility of being characterized as being in a "bad neighborhood".

Unless someone has test data, I'm not ready to buy that unless the SE is classifying an entire geographic area as a bad neighborhood.  (Not a political discussion I think they'd really want to enter into.)  Systems admins regularly implement fail over an migration scenarios that involve websites being hosted at multiple IP addresses.  I can't imagine that the SE's penalize the website when an IP address change takes place in DNS.

I don't think the IP address is an effective way to identify the value of content though and given the complications I mentioned above I suspect the SE's would agree.  My bet is they ignore it for anything other than geolocation data.

I'm willing to be proven wrong for sure!