Yes, That's Mine: Asymptotically Foolproof LLM Ownership Identification Against Hidden Adversarial Decoding Parameter Perturbations Author: Jerry Bao (Contact: jerry.bao@uwaterloo.ca) Acknowledgements: This research is supported by the Vector Scholarship in Artificial Intelligence, provided through the Vector Institute. Abstract (Draft) Creating and training an LLM can take vast amounts of resources, money, and effort. Because of this, many LLM creators seek to protect their credit and IP from being stolen. 'LLM ownership identification', the study of determining whether an anonymous LLM is a stolen version of a known LLM, is therefore one of the primary commercial, legal, and ethical motivators for the research of LLM provenance. White-box methods and backdoor-style black-box methods for LLM ownership identification face challenges with constrained practical assumptions and invasiveness, driving the search for effective and non-invasive black-box methods. There is a practice-theory gap in the current research for non-invasive, black-box methods, and we have proposed a community-wide formal program for classifying threat scenarios which admit 'theoretically foolproof' (in the sense of decidability, statistical consistency, etc.) methods of LLM ownership identification. Starting from first principles, we argued that hidden decoding parameter perturbations are the necessary first model-identity-obfuscation class to investigate for this formal program. We then constructed statistically consistent tests for identifying a black-box LLM's ownership identity under such identity obfuscations. The tests presented in this paper satisfy key desirable properties such as: 1) being non-invasive and fully black box, 2) being statistically consistent, 3) possessing asymptotically fast convergence, and 4) being viable against an adversary with perfect information. Along the way, we implicitly proved a fundamental negative result: standard, token-distribution-modifying decoding parameters are not obfuscating enough to prevent the existence of a non-invasive, theoretically foolproof method for determining a black-box LLM's ownership identity. In doing so, we established the first constructive evidence of the feasibility of the proposed formal program, which aims to prove similar results under other threat scenarios. Current status This paper is undergoing active modifications prior to submission and peer review. Its core theoretical results are stable and complete. Its presentation is expected to change significantly. Citation If you would like to cite this work, please use: Title: Yes, That's Mine: Asymptotically Foolproof LLM Ownership Identification Against Hidden Adversarial Decoding Parameter Perturbations Author: Jerry Bao DOI: https://doi.org/10.5281/zenodo.18127692 Year: 2026 TO-DO Citation formatting Restructuring and refactoring Expositional clarity and conciseness Typo correction