Time as Index: Structural Irreversibility Prior to Landauer

Trilogy Overview: Time as Index and the Landauer Interface (Paper 1 of 3) This paper establishes a formal structural framework for irreversibility that precedes thermodynamic dissipation. We define Time as Index as the monotonic ordering of irreversible updates in bounded non-closed systems. By identifying a deterministic structural residue (Slip), we show that temporal directionality arises from finite retention and failed recurrence attempts, independent of entropy. Core Result: Structural irreversibility precedes thermodynamic dissipation. Time is an index before it is a cost. This is the formal/canonical version of the trilogy.