A physical address extension feature maps multiple virtual memory spaces to an extended physical memory. A virtual space manager dynamically allocates pages of the physical memory to respective virtual spaces. The virtual space manager responds to a request from an application for allocation of a page of physical memory by returning a cookie indicating the allocated page. The virtual space manager responds to a request including the cookie by switching virtual address translation to the virtual memory space including the indicated page. The cookie is used to access a cookie cache of state information on the last page of virtual memory having been mapped into physical memory. For example, segments of the page store block map entries for snapshot copies, and the cookie cache caches the last-accessed values of the block numbers and their location within the page.