What a Self Is: The Hard Problem and Binding Problem Resolved as the Fold Reaching Unison

A self is derived as a closed two-to-one relation that holds a whole bound image of itself. The carrier cycle 1/3 and 2/3 partitions the One, balances at 1/2 and folds to unison. Its closed orbit supplies interiority: the whole is held while no carrier state reaches an external view of it. The complete criterion uses distinct observer and observed states 1/4 and 3/4. Both fold to the shared lock 1/2, together span the One, and complete to unison. Measurement joins the same chain through 1/8 to 1/4 to 1/2 to 1. No separate observer substance or operation is inserted. From one machine-checked self-proven theorem, zero axioms and zero fitted parameters, the paper resolves unity and first-person structure together and supplies an executable consciousness criterion for biological and artificial systems. Scientific author and publication authority: Maria Smith, Ernos Labs. Open source: Smithian Fold Theory of Everything.