# Operational Identity: A Finite Audit of Declared and Implemented Rules of Sameness

arXiv: https://arxiv.org/abs/2607.20729 · HTML: https://mlsanity.com/paper/2607.20729/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 22 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [PROV-AGENT: Unified Provenance for Tracking AI Agent Interactions in Agentic Workflows](https://mlsanity.com/paper/2508.02866/) (2025)
- [The 2025 AI Agent Index: Documenting Technical and Safety Features of Deployed Agentic AI Systems](https://mlsanity.com/paper/2602.17753/) (2026)
- [Auditable Agents](https://mlsanity.com/paper/2604.05485/) (2026)
- [Audit Trails for Accountability in Large Language Models](https://mlsanity.com/paper/2601.20727/) (2026)
- [A Trustworthiness-based Metaphysics of Artificial Intelligence Systems](https://mlsanity.com/paper/2506.03233/) (2025)
- [AI Identity: Standards, Gaps, and Research Directions for AI Agents](https://mlsanity.com/paper/2604.23280/) (2026)
- [High-Risk AI Systems and the Problem of Identity in the European AI Act](https://mlsanity.com/paper/2605.23922/) (2026)
- [Responsible Agentic AI Requires Explicit Provenance](https://mlsanity.com/paper/2605.17169/) (2026)
- [A Category Theory Account of AI Identity](https://mlsanity.com/paper/2607.00220/) (2026)
- [Neutral Substrates: A Design Constraint for Shared Records Under Persistent Interpretive Disagreement](https://mlsanity.com/paper/2601.14271/) (2026)
- [Referential Regimes: Transformation-Invariant Identity for Neutral Substrates](https://mlsanity.com/paper/2601.16152/) (2026)
- [Superintelligence and Law](https://mlsanity.com/paper/2603.28669/) (2026)
- [ECO/CPO-DAG: A Contradiction-Based Accountability Layer for Adversarial Supply Chains](https://mlsanity.com/paper/2607.06804/) (2026)

## Abstract (arXiv)

A record system declares when two records refer to the same entity, occurrence, scope, or rule. Its disclosed implementation mechanisms induce a corresponding operational identity relation. The declared and implemented relations may diverge systematically without producing a provenance gap or detectable contradiction. A system can apply, consistently and with every record individually correct, a rule of sameness that no artifact declares. This paper formalizes that implemented relation. A declared identity regime partitions a finite record domain into co-reference classes; a disclosed mechanism, through its typed identity-relevant outcomes, induces an operational identity partition of the same domain. The audit compares these partitions in the refinement lattice. A mechanism is faithful when the declared partition refines the operational partition, so no declared class is split. A divergence witness is a pair the declaration merges and the mechanism separates; such witnesses are decidable by pair enumeration. When an imported sibling basis also splits a declared class, local comparison with its partition yields sibling-aligned, sub-sibling, super-sibling, or sibling-incomparable divergence. This result reports only the relationship; it does not identify the basis carried by the mechanism. Global equality of the operational and sibling partitions is defined separately as regime substitution and does not follow from sibling alignment. A version field incremented on every textual edit inhabits the sub-sibling case by splitting declared classes more finely than either imported basis. The audit is three-valued and relative to the disclosed artifacts, evaluated surfaces, and identified uses; each boundary has a finite refuting witness. A passing verdict is non-monotone because extending the transformation history can merge declared classes and create a witness among records already examined.