Black and Gold V-Reversible Golden Orbits, Guardian Agents, and the Limits of the Common Gate

Reversible Golden Orbits, Guardian Agents, and the Limits of the Common Gate C. J. Tully Independent Researcher, Engineer — Tamworth, NSW, Australia ORCID: 0009-0007-5661-7332 October 2026 ABSTRACT This paper is the fifth of the black-and-gold series. It examines the bilateral golden orbit generated by the reversible scaling operator of Paper I, the conditions under which a guardian agent may apply integer powers of that operator without leaving its integrity envelope, and the precise limits of what the common Quasi-Equivalence Index gate does and does not guarantee. The orbit is algebraically reversible. Under the ordinary graded norm a bilateral orbit is bounded if and only if the state is supported in degree zero. Any coherence predicate invariant under a single application remains constant along the entire orbit. A guardian agent certified by the gate may therefore scale or contract through integral powers of φ while remaining admissible. Preservation of the index is not cryptographic security beyond the gate. Algebraic reversibility is not metric boundedness. The series remains closed under these distinctions. 1. Introduction