The appellate court's decision can be found
here(.pdf).
Having scanned the majority and dissenting opinions, I'm persuaded by the dissent. The majority has, in effect, created a new definition of "resided in" that applies only to candidates for office, and which amounts to "lived in." That's a standard that has never applied to candidates for office, for very good reasons. If a candidate were required to "live in" a district for a significant period of time (
i.e. physically reside in that district without interruption), then incumbent legislators who spend a good deal of the year in Springfield or Washington would be barred from running for reelection.
The dissent focuses -- properly, I think -- on the candidate's intent to return to the district, rather than the candidate's actual physical presence in the district. That makes sense. The majority's distinction between what constitutes "resides in" for electors and what constitutes "resides in" for candidates is, in contrast, artificial and unmanageable.
The Illinois Supreme Court's decision to take this case on an expedited appeal is, I think, a fairly good indication that the court is leaning toward reversing the appellate court and reinstating Emanuel on the ballot.