When Execution Evidence Is Not Enough: Bounded Countermodels for AI-Agent Authorization, Idempotency, and Log Continuity

A valid execution receipt, authorization grant, or audit checkpoint does not alone establish that an AI agent executed safely. This preprint investigates evidence sufficiency under incomplete observations and explicitly bounded threat models. It presents reproducible synthetic countermodels for execution-time authorization, retry and idempotency failures, concurrent operations, external side effects, downstream fan-out, and audit-log continuity. Four finite-world grammars enumerate 20 histories. A reproducible Python research suite contains 104 unit tests, successfully executed on Python 3.10, 3.12, and 3.13. The contribution is an auditable technical countermodel corpus and claim-to-evidence framework. Results are conditional on stated assumptions and do not constitute production security certification or a new general impossibility theorem. Not peer reviewed. Reproducibility: Research software version 1.2.0, DOI: https://doi.org/10.5281/zenodo.23783618 AI-assisted tools were used in research preparation, coding, LaTeX drafting, and editorial work. The named author approved the scientific text and accepts responsibility for the content.