The floors
should be fire-resistance rated since a sprinklered A-3 (library) occupancy on the 4th floor (yes, the three floors of the library are above a first-floor shop) needs to be Type III-A, II-A, or Type I. That the floors and columns have no fire-resistance rating is another story entirely (short answer: there was a prior NYS Code Variance).
So the floors are not fire-rated, but Section 711.3.2 still requires continuity except as permitted by Section 712. But Steveray is right: I should not have referenced Section 711.2 for the continuity requirement.
Reading the 2015 IBC Code Commentary, I'm getting mixed signals. On the one hand, the Commentary seems to suggest that spaces adjacent to the atrium can be considered part of the atrium, even if they do
not meet other requirements in Section 712, as long as they meet the atrium provisions (basically for smoke control). But on the other hand, the smoke control rationale for atriums seems to be violated by suggesting that these three open stories—with permeable floor-ceiling assemblies that do
not meet the other provisions of Section 712—are part of the atrium. Here's the relevant Commentary passage: "Exception 3 recognizes the desire to have at least some floors open to the atrium, and permits a maximum of three. ... The exception also states that the smoke control design must account for these spaces. This particular reference to the smoke control design does not require that the 6-foot-high (1829 mm) layer required by Section 909.8.1 be maintained in these spaces. Instead it is saying that if a smoke control system is required by Section 404.5,
such spaces must be accounted for in terms of the hazard they pose to the atrium and to smoke migrating to other adjacent spaces or other stories open to the atrium. Essentially these spaces have simply increased the possible design fires that may send smoke into the atrium, thus threatening to send smoke throughout the building and other adjoining spaces."
In other words, the Commentary seems to envision adjacent spaces
outside the atrium boundary that can be considered part of the atrium from the standpoint of smoke control. Such spaces do not intrinsically threaten adjacent spaces since any smoke originating from those spaces is directed into the atrium's smoke control system, where it stays in the vertical opening of the atrium. But in the condition I'm concerned about, with the three stories actually
within the boundary of the atrium, smoke originating in one of the lower library stack stories would not be directed into the atrium's vertical opening, but would rise directly through the open floor-ceiling assemblies into the other adjacent library spaces.
I believe that this particular scenario was not envisioned when the atrium Code rules (or the Commentary) were written.
BTW, anyone wanting to look at floor plans of this library can see them
at https://aap.cornell.edu/about/campuses-facilities/ithaca/mui-ho-fine-arts-library/project-details