Formal Specification of Information Visibility and Deterministic State Transitions in Ethereum

Abstract

Ethereum is a transactional singleton machine with a shared state defined by deterministic transitions. A fundamental separation exists between internal determinism and external visibility due to asynchronous network propagation. Transaction information traverses intermediate visibility states within a peer-to-peer gossip network before achieving broad acknowledgment. Canonical visibility and finalized commitment are contingent upon consensus-layer block collation and head-of-chain selection.

Introduction

Distributed ledger models are often discussed as if transaction visibility were a simultaneous broadcast that yields uniform observability across participants. Ethereum does not satisfy this assumption. It disseminates transaction-related information through a peer-to-peer gossip network in which messages traverse heterogeneous paths.

Because the network lacks a global clock, nodes form local views of pending transactions based on arrival time rather than a shared temporal reference. Visibility is therefore non-uniform, transiently inconsistent across nodes, and sensitive to propagation conditions and implementation details (e.g., peer management, message prioritization, and buffering).

This document records the system properties that produce a temporal gap between (i) deterministic execution of valid state transitions and (ii) externally observable, canonical commitment. The following sections define the system model, enumerate visibility states, and formalize the transitions by which transaction information reaches finalized commitment.

I. Definitions

• Visibility: The extent to which transaction-related information is observable across network nodes or external observers.

• Determinism: The property that, once a transaction is valid and executed, its resulting state transition is fixed by protocol rules.

• State (σ): The world state mapping addresses to account data.

• Transition: The process that morphs the system from one state to another via transaction execution (Υ) or block application (Π).

• Commitment: The point at which consensus finalization renders a state transition part of the irreversible canonical history.

II. System Model

Ethereum is a transactional singleton machine with a shared world state. Transaction-related information is disseminated via a peer-to-peer gossip network rather than instantaneous broadcast. In the absence of a global clock, propagation is asynchronous and produces temporal asymmetry in what different nodes observe at the same wall-clock moment.

Visibility is influenced by network-level variables (latency, routing topology, congestion) and node-level variables (peer selection, buffering, prioritization). These variables do not change the protocol definition of correctness, but they do affect when information becomes observable to different nodes and, later, to external observers.

III. Visibility States

Transaction information moves through temporally ordered phases defined by visibility:

1. Locally Known
   Information is restricted to the originating node (or an initial receiving node). Visibility is local.

2. Partially Propagated
   Information traverses heterogeneous network paths. Visibility is limited to a subset of nodes, varying with routing policies, latencies, and local processing.

3. Globally Acknowledged
   Information is widely distributed across the gossip network and present in many nodes’ local buffers, but remains pending block-level transition.

4. Canonical Visibility
   Observability becomes globally consistent only after the information is included in a block recognized as canonical by the consensus layer.

IV. State Transitions

A transaction induces state change through a structured transition process:

• Intrinsic Validation
  A transaction must satisfy validity constraints (including well-formed encoding, signature validity, and sufficient balance for up-front costs) before execution can proceed.

• Initial Transition (σ₀)
  Execution begins with an irrevocable state update that increments the sender’s nonce and applies the up-front cost accounting.

• Provisional State (σᴾ) and Accrued Substate (A)
  Execution deterministically produces an internal provisional state and accumulates an accrued substate A. The accrued substate captures execution artifacts (e.g., logs and other internal bookkeeping) generated during the transition.

• Block-Level Transition (Π)
  Transactions are collated into blocks. The block-level transition function applies collated transactions sequentially to the prior canonical state.

V. Determinism vs. External Visibility

Internal determinism is achieved once a valid transaction enters execution and reaches the initial transition point (σ₀). From that point onward, the resulting transition is governed by protocol rules and is deterministic with respect to the executing state.

External visibility, however, is delayed by propagation and by the additional requirement of canonical commitment. A temporal gap therefore persists between deterministic execution and globally consistent observability. Canonical visibility is obtained only when the consensus layer identifies a block as part of finalized canonical history; until commitment, competing canonical candidates may exist and visibility remains provisional.

Closing Note

This record isolates the system-level separation between determinism and visibility in a distributed transaction network. The gap is a structural consequence of asynchronous propagation and consensus commitment, not a behavioral assumption about observers.