The third horn is a fake, being capable of being defined in or out of existence at will. It I am indifferent to my state ten seconds from now, it is true; if my current utility function includes a term for my state ten seconds from now, it is false.

The 'thread of subjective experience' is not the issue; whether I throw myself of the cliff, will depend on whether I am currently indifferent as to whether my future self will die.