Chapter 21: Global Defect Exhaustion

Chapters 21 and 22 established the Categorical Second Law and the entropy splitting S = S_def + S_ref. Defect entropy decreases monotonically, and the contraction factor (1 - ι_τ) ≈ 0.6587 controls the rate. But a monotonically decreasing sequence might never reach zero—it could approach an asymptote. This chapter proves that it does not.

The Global Defect Exhaustion Theorem states that the total defect budget of the universe is finite and is exhausted in finitely many orbit steps. The coherence horizon n_coh—the orbit depth at which S_def first vanishes—is not merely a limit but a realized value. Irreversibility is not eternal; it has a definite end.

The proof uses two ingredients: the geometric contraction of defect support (Lemma [lem:ch21-geometric-contraction]) and the discreteness of the defect bundle lattice. Because defect bundles are discrete objects—integer-counted excitations on a lattice—their count cannot decrease continuously. When the contracted count drops below one, the last defect is absorbed, and S_def jumps to zero.