Target-Specific Safe Reconstruction under Adversarial Faults: Exact Finite Certificates and Diagnostic Complexity

Target-Specific Safe Reconstruction under Adversarial Faults: Exact Finite Certificates and Diagnostic Complexity This preprint investigates target-specific reconstruction, safe diagnostic decision-making, and robustness against adversarial observation faults within an explicitly stipulated finite twelve-state model. The framework distinguishes three reconstruction objectives: determining a safe action, identifying a recovery profile, and reconstructing the complete hidden state. For adaptive diagnostic strategies subject to at most one adversarial bit substitution, the exact minimax observation depths are 3, 5, and 9 for the three respective objectives. The corresponding nonadaptive minima are 3, 6, and 12. For a separate fault model permitting at most one arbitrary whole-domain replacement, the minimum numbers of additional independently corruptible binary observation domains are 2, 3, and 3, respectively. These lower bounds apply to arbitrary binary functions on the stipulated state space and are attained by explicit XOR-based constructions. The study further investigates restricted reversible diagnostic protocols and their implementation costs. Exact exhaustive enumeration identifies a trade-off for full-state reconstruction between three additional domains requiring nine basic reads and four additional domains requiring eight basic reads. Within the specified protocol catalogue, at least one three-input parity protocol is necessary for full-state reconstruction using only three additional domains. The mathematical results are supported by explicit finite certificates, exhaustive combinatorial searches, robust decoding checks, and two separately implemented Python verification programs. Both programs use only the Python standard library and can be executed offline. The results are conditional on the stated finite model, transition rules, observation functions, and fault-domain independence assumptions. They do not establish physical diagnostic safety, empirical recoverability, hardware-level fault independence, or general mathematical novelty. The release includes the manuscript, LaTeX source, Python verification programs, execution logs, proof and literature audits, licensing information, and an explicit declaration of AI assistance. This is an author-approved, non-peer-reviewed mathematical preprint, version 1.0, released on 10 November 2026. The reported results concern an explicitly defined finite twelve-state model. The adaptive and nonadaptive bit-error models are distinct from the whole-domain adversarial replacement model. The two included Python implementations provide separately coded computational verification, but do not constitute independent external peer review. The original manuscript and supplementary prose are distributed under Creative Commons Attribution 4.0 International (CC BY 4.0). The original Python source code is distributed under the MIT License. No claim of experimentally demonstrated safety, physical recoverability, hardware-level fault independence, or established general mathematical novelty is made. Declaration of AI Assistance OpenAI ChatGPT was used extensively during the development of this research, including mathematical exploration, finite-model design, Python programming, verification strategy, computational certificate construction, literature discovery and assessment, proof exposition, bibliographic checking, and manuscript preparation. The human author, Ivo Vajc, reviewed the research materials, tested the computational programs, examined the reported results, and authorized preparation of the final public release. The two verification programs were developed within the same AI-assisted research workflow. Their agreement provides computational cross-verification but does not constitute independent third-party peer review. Responsibility for the scientific content, interpretation, bibliographic accuracy, and publication decision remains with the named human author. Author Approval and Publication Authorization Ivo Vajc, Independent Researcher, ORCID 0009-0005-5145-6491, confirms that he has reviewed the manuscript and associated research materials, tested the supplied computational programs, and authorized the public release of the preprint: Target-Specific Safe Reconstruction under Adversarial Faults: Exact Finite Certificates and Diagnostic Complexity Version: 1.0 Authorization date: 10 November 2026 The author accepts responsibility for the decision to publish the work, including the declared scientific limitations, licensing conditions, and disclosure of AI assistance. This declaration records the author's expressed authorization and does not constitute an independently authenticated digital signature.