Chronology as a Consistency Invariant in Composable Information Systems

Abstract

We formalize a minimal setting in which a chronology (a strict partial order on events) is forced by consistency of distributed information under local composability. The system maintains distributed records interpreted as constraints over a global possibility space (Omega, Sigma), optionally with a measure mu. Events act locally by monotonically tightening records, and independent events commute (diamond/trace semantics), yielding schedule invariance. We define operational influence without assuming primitive time: e influences f if executing e can change what constraint f writes on a shared site. Influence cycles alone need not imply inconsistency, so we distinguish weak influence (dependence) from strong influence (exclusive branching on an observable predicate). Assuming global satisfiability of all reachable record states, the diamond property, monotone information writing, and a mild branch-determinacy axiom for witnessed exclusivity, we prove that strong influence is acyclic and therefore induces an intrinsic chronology. We also show trace invariance and minimality of the derived order, introduce a monotone information clock based on -log mu(feasible set), and give an escape taxonomy: any model that admits strong-influence cycles without inconsistency must violate global consistency, local composability, monotone writing, or branch determinacy.