> It is my understanding that 2k cores are real, and 2k+1 is their matching, "virtual" core)

I'm not sure that's true. For example, on a i7-4770 I get:

  $ cat /sys/devices/system/cpu/cpu[0-3]/topology/thread_siblings_list
  0,4
  1,5
  2,6
  3,7

(Of course, that might just be Linux renumbering them)