General Theory of Finite Descent Authority

his preprint introduces the General Theory of Finite Descent Authority (GTFDA), the finite authority-gate layer of the Omega Tower framework. The central claim is that a proposal does not acquire operational authority merely by existing, being routed, being represented, being fluent, or fitting a broader theory. Instead, operational authority arises only when a proposal descends into a finite certified packet with declared carrier, candidate class, verifier, terminalizer, and lift/refusal discipline. The paper formalizes authority as an inhabited dependent record: Authority (p): = Σ (t: Tₐuth) (Π# (p) = inl (t) and develops the pipeline: proposal -> sector -> realization -> finite packet -> verified fiber -> terminat type -> authority/refusal GTFDA distinguishes proposal, routing, realization, descent, verification, and terminalization. It argues that raw answers, model fluency, confidence, majority vote, route success, fallback behavior, local obstruction evidence, and global theoretical structure do not by themselves constitute authority. Authority is carried only by terminalized verified descent, while failed realization, missing packets, incomplete search, ambiguous fibers, and unsupported lifts return typed non-authority terminals such as BudgetUnknown, NoRule, NonUnique, TypedRefusal, LiftRequired. The paper also clarifies the relationship between GTFDA and the General Theory of Finite Obstruction Calculus (GTFOC): GTFOC supplies local obstruction evidence, while GTFDA determines when such evidence terminalizes into operational authority or refusal. LLM outputs are treated as proposals requiring finite replayable trace packets, not as authority-bearing objects in themselves. This version is a publication spine and preprint. Some claims are definitions or prose-proof theorems, while observer-capable and symbolic-selection material remains conditional or open. Commercial implementation details for Anomalon AI are intentionally excluded.