Normalization Confluence for Registry-Governed Stream Processing

Coordination-free convergence in distributed systems has been achieved through two structural regimes: operation commutativity (CRDTs) and invariant confluence (I-confluence). This paper identifies a third regime — normalization confluence — in which operations may be non-commutative and may violate application invariants, but convergence is restored through a compensation operator that normalizes states to validity.

We formalize this regime by introducing registry-governed stream processing, where an external registry of invariant predicates defines valid states and a compensation operator repairs violations. We construct a governance rewrite system and prove, via Newman's Lemma, that two structural conditions — well-founded compensation (WFC) and compensation commutativity (CC) — guarantee that all causality-respecting processing orders yield the same valid state. We prove both conditions are necessary: without WFC, compensation depth is unbounded; without CC, different orders reach different valid states.

Compensation commutativity is strictly weaker than operation commutativity: operations need not commute, only their compensated results. To make CC practically verifiable, we develop a verification calculus based on invariant footprints and decomposable repair that reduces the global CC obligation to local, per-event-pair checks, together with a product composition theorem for modular verification.