arXiv:2607.20729cs.LOcs.AI2026-07

研究记录系统中声明与实际身份关系的差异,发现二者可能不一致却无法被察觉。

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

  • 通过形式化声明与实际身份划分,建立审计框架对比两者差异。
  • 发现系统可一致应用未声明的身份规则,且差异可通过配对枚举验证。
  • 适用于需要精确追踪数据同一性的系统审计,如数据库或知识图谱。

记录系统声明两个记录是否指代同一实体、事件、范围或规则。其公开的实现机制会导出相应的操作性身份关系。声明与实现的关系可能系统性地偏离,但不会产生溯源断层或可检测的矛盾。系统可以一致且每个记录均正确地应用一条未被任何实体声明的身份规则。本文形式化了该实现关系。声明的身份制度将有限的记录域划分为共引用类;公开机制通过其类型化的身份相关结果,诱导出同一域的操作性身份划分。审计在细化格上比较这两个划分。当声明划分细化操作性划分时,机制是忠实的,即无声明类被拆分。分歧证人是一对被声明合并而机制分离的记录;此类证人可通过配对枚举判定。当导入的兄弟基也拆分一个声明类时,局部比较其划分可得兄弟对齐、子兄弟、超兄弟或兄弟无关分歧。此结果仅报告关系,不揭示机制所携带的基。全局操作与兄弟划分相等定义为制度替代,不必然由兄弟对齐推出。每次文本编辑递增版本字段,在子兄弟情形下比任一导入基更细地拆分声明类。审计为三值,相对于公开的实体、评估表面和识别用途;每条边界均有有限反例。通过判决非单调,因为扩展转换历史可能合并已检查记录的声明类并生成新证人。

原文摘要 · Abstract (English)

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.

身份识别系统审计数据一致性

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