@contrex,
Terry is in the library.
At this point in time, Terry is in the library.
Terry may be in the library.
(a) Terry has permission to be in the library.
(b) It is possible that Terry is in the library at this point in time.
Terry might be in the library.
It is possible that Terry is in the library at this point in time.
Terry might have been in the library.
It is possible that Terry has been in the library at some point in the past.
You forgot the one time use.
Terry could be in the library.
It is possible that Terry is in the library at this point in time.
Terry can be in the library.
(a) Terry has permission to be in the library.
(b) It is possible that Terry is in the library at this point in time.
You've lumped 'can/could/may/might' all together. If they all had identical meanings, English would have no need of three of the four.
Is 'can' used for these one time specific senses, C? It doesn't sound quite right, except as, possibly, a strong assertion to counter a denial.
Terry should be in the library.
Terry ought to be in the library.
You forgot deontic 'should/ought to'
Terry will be in the library.
At some time in the future, Terry will be in the library.
You forgot the now of 'will'.