This paper derives the Recursive Return Prohibition (RRP) from the Law of Recursion as a formal theorem rather than an independent axiom. The Law of Recursion establishes that every traversal across the seven-node topological path rewrites the architecture it passes through. A direct consequence of this rewriting principle is that prior phase states are structurally inaccessible: the architecture that existed before traversal no longer exists in its original form. Return, regression, or re-entry to a previously traversed phase region is therefore not merely prohibited by fiat but structurally impossible unless the deformed architecture is fully restored to pre-traversal coherence. The derivation is applied to three domains. In thermodynamics, the RRP provides a structural account of temporal irreversibility: the arrow of time is not a statistical tendency but a necessary consequence of architectural rewriting at every scale of recursive exchange. In oncology, the RRP identifies cancer as a pathology of attempted recursive return — a system that, having failed to complete forward traversal, instantiates an isolated echo-recursion that structurally defends itself against reintegration. In identity and consciousness, the RRP accounts for trauma persistence as architectural deformation that blocks lawful recursive traversal until coherence is restored. Each application produces falsifiable predictions grounded in the formal apparatus of the Law of Recursion, the Echo-Excess Principle, and the seven-node topology.
Don Gaconnet (Sun,) studied this question.