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

Fernando Paredes García

cs.DCApr 5, 2026

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

Authors: Fernando Paredes García

Organizations: Independent Researcher

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 Grassé 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 (Coordinación indirecta basada en el estado del registro contable) as a ledger-specific applied definition that maps Grassé'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.

Figures & tables

Concept	Key Source(s)	Role in Our Definition
Original stigmergy	Grassé (1959) [ 1 ]	Indirect coordination via environmental traces.
Swarm intelligence	Dorigo et al. (1996) [ 3 ] and Bonabeau et al. (1999) [ 4 ]	Computational viability of stigmergic optimization and digital pheromone trails.
Universal stigmergy	Heylighen (2016a, 2016b) [ 6 , 7 ]	Four-component decomposition we map onto ledger primitives.
Tuple spaces	Gelernter (1985) [ 11 ]	Shared associative memory as coordination substrate.
Coordination artifacts	Omicini et al. (2004) [ 15 ] and Weyns et al. (2007) [ 14 ]	Environment-embedded coordination objects that support our smart-contract reading.
Blockchain state machine	Wood (2014) [ 18 ] and Garay et al. (2015) [ 30 ]	Formal state-transition semantics for the medium.

Table 1: Literature mapping: concept, source, and role in our definition

Stigmergy	Heylighen (2016)	Ledger Counterpart
Medium	Shared environment where traces persist	Ledger state: world state $\sigma$ (storage, balances) + event logs $\mathcal{L}$
Trace	Persistent modification left by action	State transition $\delta(S_{t},a)$ producing $S_{t+1}$ ; emitted events $e\in\mathcal{L}$
Agent	Autonomous entity that acts and perceives	EOA-controlled bot, smart contract actor, keeper, MEV searcher
Stimulation rule	Trace triggers subsequent action	Predicate $\mathcal{P}_{i}(S_{t})\rightarrow$ act: agent $i$ reads state, checks condition, submits tx

Table 2: Stigmergy

\rightarrow

ledger mapping

Pattern	Signal	Activation	Gas	Delay	Main Threat
State-Flag	Storage var.	Bool/enum	Low	1 block	Frontrunning
Event-Signal (hybrid)	Log entry	Subscription	Med.	1 block+	Spam, reorgs
Threshold	Numeric var.	Inequality	Med–High	1 block	MEV, oracles
Commit-Reveal overlay	Two-phase	Phase-gated	High ( $\sim$ 2 $\times$ )	$\geq$ 2 blocks	Non-reveal

Table 3: Comparison of ledger-state stigmergy base patterns and sequencing overlay

Style	Trust	Contention	Recovery locus	Transparency	Infra. dependency
STIG	Ledger consensus plus contract rules	High when many agents react to the same visible trace	On-chain medium: expiry, timeout, staking, slashing	High; traces and recovery logic are protocol-visible	Ledger plus practical RPC/indexing reliance for observation
MSG	Reliable off-chain coordination channel	Lower if negotiation succeeds before submission	Off-chain coordination and participant retry	Medium; agreement happens outside the ledger	Ledger plus messaging infrastructure
ORCH	Trusted scheduler or operator	Lowest in benign operation; scheduler bottlenecks remain	Central scheduler and its operational procedures	Low–medium; assignment logic is external	Ledger plus orchestrator service

Table 4: Analytical comparison of coordination styles for the task-board witness

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