A Fixed-Point Theory of Admissible Trajectories: From Viability Kernels to Pre-Execution Ontological Gates (AGDAU Core)

Abstract We present a formal theory of admissibility-as-existence for controlleddynamical systems, intended as a foundational layer for the safe deploymentof autonomous and multi-agent AI systems at scale. The core mathematical result identifies admissible long-horizon behaviorwith the greatest fixed point of a monotone admissibility operator on thepowerset lattice of states. This fixed point is shown to coincide exactlywith the viability kernel: the set of states from which at least one policycan maintain constraint satisfaction indefinitely. We then connect this fixed-point characterization to an execution-levelarchitecture. A pre-execution admissibility gate defines the executableaction set A^{exec}(s) and enforces the inclusion A^{exec}(s) ⊆ A*(s; K), where K is the admissible state constraint set. Under this architecture,unsafe trajectories are not discouraged, penalized, or corrected post hoc;they are structurally non-executable. Finally, we formalize Strict I5 traceability (“No Trace—No Action”) as anecessary condition of executability, yielding observability,auditability, and falsifiability as intrinsic properties of the executioninterface itself. The resulting chain Law-Spec → EAG → Trace Schema (I5) → RCL → AGDAU-lint is closed, enforceable, and suitable for standardization and regulatory use. Files included in this record: 1. paper_v1.1_canonical.pdf – Canonical formatted publication (primary reference). 2. paper_v1.1_canonical.tex – LaTeX source corresponding exactly to the canonical PDF. 3. paper_v1.1_canonical.txt – Plain-text canonical version for archival, indexing, and long-horizon preservation.