The Final Time is a theoretical paper on contingent singularity and the material viability of historical exteriority. It shifts singularity theory away from recursive intelligence growth and toward the conditions under which a contradiction can persist, transmit, activate, and reproduce as an independent historical relation. The paper develops a monetary-infrastructural-symbolic sovereignty vector for durable exteriority under monetary allocation, derives a regime-dependent diminishing dialectic from viability-kernel contraction, and replaces the assumption of one necessary successor with a field of competing contingent Omegas. It distinguishes terminal closure, where no exterior rival retains a viable route to durable standing, from terminal reflexivity, where an order becomes durable while preserving the possibility of its own future negation. Machine semantic labor, persistence, recognition versus binding, shared carriers, and the operational sum Logos are treated as the contemporary architecture in which these conditions become materially testable. This deposit seats the complete v0.5 text, including the empirical program's persistence, deletion-history, master-degradation and viability-kernel tests, the statement of what the paper does not claim, the conclusion on the next turn, and the formal dictionary and source appendices; it supersedes #1635, whose seated text ends at §36.2.