Ledger-State Stigmergy: A Formal Framework for Indirect Coordination Grounded in Distributed Ledger State

TL;DR

This paper introduces a formal framework for indirect coordination among on-chain agents using shared ledger state, bridging swarm intelligence concepts with blockchain technology.

Contribution

It provides a ledger-specific formalization, identifies core coordination patterns, and offers design guidance for decentralized on-chain coordination.

Findings

Identified three recurring on-chain coordination patterns: State-Flag, Event-Signal, Threshold-Trigger.

Developed a formal state-transition model for ledger-based indirect coordination.

Compared ledger-state coordination with off-chain messaging and centralized control in a task-board example.

Abstract

Autonomous software agents on blockchains solve distributed-coordination problems by reading shared ledger state instead of exchanging direct messages. Liquidation keepers, arbitrage bots, and other autonomous on-chain agents watch balances, contract storage, and event logs; when conditions change, they act. The ledger therefore functions as a replicated shared-state medium through which decentralized agents coordinate indirectly. This form of indirect coordination mirrors what Grass\'e called stigmergy in 1959: organisms coordinating through traces left in a shared environment, with no central plan. Stigmergy has mature formalizations in swarm intelligence and multi-agent systems, and on-chain agents already behave stigmergically in practice, but no prior application-layer framework cleanly bridges the two. We introduce Indirect coordination grounded in ledger state (Coordinaci\'on indirecta basada en el estado del registro contable) as a ledger-specific applied definition that maps Grass\'e's mechanism onto distributed ledger technology. We operationalize this with a state-transition formalism, identify three recurring base on-chain coordination patterns (State-Flag, Event-Signal, Threshold- Trigger) together with a Commit-Reveal sequencing overlay, and work through a State-Flag task-board example to compare ledger-state coordination analytically with off-chain messaging and centralized orchestration. The contribution is a reusable vocabulary, a ledger-specific formal mapping, and design guidance for decentralized coordination over replicated shared state at the application layer.