Deployable and Insurable AGI Requires Verifiable Execution Admissibility: A Conditional Bounded-Loss Theorem for Agent Systems

AbstractWe present an audit-grade formal framework for deployability and insurability of AGI-class and high-capability autonomous agent systems based on verifiable execution-admissibility constraints. The framework introduces a strict separation between capability generation and real-world execution. Capability is modeled as an unconstrained action generator, while environment-affecting execution is mediated by a stochastic execution-admissibility gate enforcing non-bypass receipt semantics, adapter-closed effect channels, fail-closed decisions, context binding, and policy-bounded execution cones over measurable state–action space. We prove two complementary formal results. First, an unbounded-loss lemma under bypassable execution surfaces, showing that if effectful actions can occur outside verifiable admissibility control with nonzero probability, no finite upper bound exists on expected executed loss. Second, a conditional bounded-loss theorem under machine-verifiable execution-admissibility invariants, risk-tiered gate soundness error budgets, adapter-class loss caps, and residual bias bounds. The resulting deployability bound is independent of capability generator structure and depends only on execution control surface geometry and verified error parameters. The results provide a formal and audit-ready basis for deployability and insurability analysis of AGI-class and high-capability agent systems under execution control layers. Claims are conditional, invariant-based, and evidence-bound. Scope is explicitly limited to effectful execution risk and does not cover semantic, persuasion, or non-effect information harms. This Zenodo record includes a reproducible publication package containing aligned versions of the same work in multiple formats: — the canonical publication PDF (audit-grade formatted version)— the full LaTeX / Overleaf source version (main .tex)— a plain-text DOI-ready version with identical technical content All included documents are content-identical at the theorem, definition, and invariant level and are provided to support reproducibility, audit review, citation, and standards-style evaluation workflows. Author: Khamikoev, Aslanbek YurievichContact: ai.hdr.technology@gmail.com