Chapter 4: τ-Distinction: The Self/Non-Self Boundary

The formal τ-distinction predicate D: X → 2τ is defined by five conditions: clopen, refinement-coherent, eventually stable, law-stable, and H∂-equivariant. Three carrier families—finite-lineage (biological), macro-torus (black hole), and galactic (basins)—realize the framework at different scales. Two canonical modes connect boundary geometry to defect thermodynamics. The Distinction Well-Definedness Theorem establishes that τ-finiteness of the carrier at each refinement level ensures the predicate terminates.