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

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.