Chronology as a Consistency Invariant in Composable Information Systems

TL;DR

This paper formalizes a minimal framework where a consistent chronology emerges from distributed information systems, using influence relations and monotone information constraints, ensuring schedule invariance and minimality of the derived order.

Contribution

It introduces a formal model linking influence cycles to intrinsic chronologies in distributed systems, with conditions ensuring acyclicity and consistency.

Findings

Strong influence is acyclic under certain axioms.

Derived order is minimal and schedule-invariant.

Models with influence cycles must violate key system properties.

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.