Consensus as Collapse Policy: Communication Evidence, Horizons, and Prefix Decisions

Jul 16, 2026

Upload by Oliver

Consensus protocols are usually specified by terminal artifacts such as decided values, replicated logs, or finalized prefixes, but that view conceals the communication-derived evidence that makes these outputs safe. This paper models distributed execution as an order-2 evidence state induced by communication and interprets classical consensus outputs as order-1 projections of that state. It compares protocols as collapse policies, separating legitimacy of evidence from the policy that determines when preserved distinctions may stop mattering, and links this distinction to impossibility results and structured carriers.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages48

Reading Time2 h 1 min

Abstract

Introduction

Consensus as an output-first vs communication-first view

Communication-history reading and carriers

Lamport’s happened-before as a projection analogy

Comparing protocols via collapse policy

arXiv :2607 . 10152v1 [ cs .DC] 11 Jul 2026 Consensus as Collapse Policy: Communication Evidence, Horizons, and Prefix Decisions Tomislav Grospić [grospic@gmail.com](grospic@gmail.com) July 2026 Abstract Consensus protocols are usually specified by their terminal artifact: a decided value, replicated log, or finalized prefix. This output-first view hides the communication-derived evidence that makes such artifacts safe: messages, votes, certificates, causal dependencies, equivocation evidence, timeouts, and local views. This paper makes that carrier explicit. We model distributed execution as an order-2 evidence state induced by communication and read classical consensus outputs as order-1 projections of that state. Under this view, consensus protocols can be compared as collapse policies. A protocol specifies which evidence is legitimate, which finite horizon it inspects, when it projects a communication-induced evidence state into a value or prefix, and how it repairs or defers collapse when the visible evidence is insufficient. This separates legitimacy from collapse: quorum intersection, committee eligibility, checkpoint votes, sampling confidence, estimator safety, or DAG support can make evidence decision-grade, while the collapse policy determines when preserved distinctions are allowed to stop mattering. The impossibility lineage supports the same distinction. FLP constrains deterministic guaranteed collapse to a terminal decision under full asynchrony with one crash failure; set agreement exposes the width of the output carrier; topological distributed computing characterizes when a history/view carrier admits a structure-preserving map to an output carrier. The contribution is therefore not a new impossibility theorem or a replacement for protocol-specific proofs, but adenotational specification framework: consensus is collapse under evidence. 1 Introduction Consensus is commonly presented as the problem of making distributed processes agree on a single value. That definition is correct for the classical task: agreement, validity, and termination are stated over a terminal decision [5] . But concrete protocols do not begin with a decided value. They begin with proposals embedded in communication. Processes exchange messages, form local views, collect votes, detect equivocation, wait for rounds or waves, build certificates, follow leaders, and sometimes defer decisions through fallback rules. This paper studies the structure that appears before the terminal decision. The central claim is simple: Nontrivial consensus is lawful projection from communication history: protocols differ less in their terminal artifact than in their policy for making accumulated communication evidence legitimate, visible, and stable enough to collapse into an order-1 output. In many protocols, legitimacy is supplied by an intersection or threshold condition. In crashfault protocols such as Paxos and Raft, majority quorums intersect, so a later leader can recover the value or log prefix that may already have been made durable [2, 4] . In Byzantine quorum protocols, the boundary is stronger: with n = 3f + 1, any two quorums of size 2f + 1 intersect in at least f + 1 validators, hence in at least one correct validator. Weighted quorum systems, resource-weighted systems, and flexible quorum systems change the unit being counted or the pairs of quorums that must intersect. Federated quorum slices, private committee sortition, stable-prefix rules, finality gadgets, and repeated sampling change how decision-grade evidence is carried, but they still give the collapse rule a structured carrier to read. The real variation lies in the carrier and its closure policy. Protocols choose how much communicationinduced evidence to preserve before output, how they compress that evidence, when they stop waiting, and what they do when the visible evidence is insufficient. The same pattern is already visible in the original Byzantine

FAQs

What does the paper mean by viewing consensus as a “collapse policy”?

It treats consensus as a process that collapses a communication-induced evidence state into an order-1 output (value, log, or prefix) only when the accumulated evidence is made legitimate, visible, and stable enough.

How are distributed execution and consensus outputs modeled in this framework?

Distributed execution is modeled as an order-2 evidence state induced by communication, while classical consensus outputs are read as order-1 projections of that state.

How does the paper relate quorum-based protocols to the collapse boundary?

Quorum conditions (e.g., quorum intersection and eligibility rules) supply legitimacy-grade evidence, while the protocol’s closure policy determines how much evidence is preserved, when waiting stops, and how collapse is repaired or deferred when evidence is insufficient.

Jul 16, 2026

Upload by Oliver