[Non-Sequitur]

Or in the admission of States to the Union, or in secession.

Admission? No. But once a state has been allowed to join then the Supreme Court has original jurisdiction over all cases in where a state may be a party. That includes illegal attempts at secession.

[Who is John Galt?]

...once a state has been allowed to join then the Supreme Court has original jurisdiction over all cases in where a state may be a party.

Wrong (as usual):

AMENDMENT XI

The Judicial power of the United States shall not be construed to extend to any suit in law or equity, commenced or prosecuted against one of the United States by Citizens of another State, or by Citizens or Subjects of any Foreign State.

Of course, I have no doubt that you could rationalize some sort of 'implied' power that would negate the clear, written words of the Eleventh Amendment - just as you've done for the Ninth & Tenth Amendments...

;>)