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

• URL: http://arxiv.org/abs/2607.20729v1
• Date: Wed, 22 Jul 2026 21:02:37 GMT
• Title: Operational Identity: A Finite Audit of Declared and Implemented Rules of Sameness
• Abstract summary: A system can apply consistently and with every record individually correct, a rule of sameness that no artifact declares.<n>A declared identity regime partitions a finite record domain into co-reference classes.<n>A disclosed mechanism induces an operational identity partition of the same domain.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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