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The End of Consensus Research?

Clément Burgelin, Rachid Guerraoui, Zicong Hong, Yinan Hu, Anne-Marie Kermarrec, Rafael Pires, Rasmus Moorits Veski, Martijn de Vos

arXiv:2610.30114v1cs.DCcs.AI

TL;DR

Consensus research still faces the challenge of discovering practical low-latency protocols that combine protocol knowledge, correctness, implementation, and evaluation. The paper presents AI-GREEMENT, a domain-specific agent harness, and A-GREEMENT, a new protocol. A-GREEMENT improves mean latency on write-heavy and read-heavy workloads and matches the best baseline on read-only workloads, while the authors maintain that human experts remain essential.

  • Problem

    Discovering practical, low-latency consensus protocols remains challenging because protocol knowledge, correctness reasoning, implementation, and experimental evaluation must be integrated.

    Source: §1 · p. 1

  • Method

    AI-GREEMENT equips coding agents with a consensus knowledge base, modular implementation skeleton, and LEAN-based verification framework, and is used to discover A-GREEMENT.

    Source: §1 · p. 2

  • Results

    12.2% and 33.3% lower mean latency than the best alternative on write-heavy and read-heavy workloads, respectively, with A-GREEMENT matching the best-performing baseline on read-only workloads.

    Source: §1 · p. 3

  • Takeaways & Limitations

    AI agents can take on substantial parts of consensus research, but human expertise remains essential for setting objectives and requirements, designing evaluations, and reviewing outcomes.

    Source: §10 · p. 18

    General-purpose agents' search improvements were limited in part by missing consensus-design knowledge, reusable implementation support, and formal verification beyond tested executions.

    Source: §2.3 · pp. 4–5

Abstract

from arXiv · show

Consensus is a fundamental problem in distributed computing and at the core of state machine replication (SMR). Despite decades of active human research, discovering practical low-latency solutions to the problem is still open, as it requires combining protocol knowledge, correctness reasoning, implementation, and experimental evaluation. We report on how AI helped us discover A-greement, a new consensus protocol for geo-replicated state machines that significantly outperforms state-of-the-art solutions. Averaged across six deployments with 5 or 9 replicas, A-greement reduces the mean latency of a geo-distributed key-value store over the fastest baseline by 12.2% and 33.3% on write-heavy and read-heavy workloads, respectively, and matches the fastest baseline on read-only workloads. A-greement combines lease-authorized local reads, direct client learning for leader-ordered writes, and a fast fixed-quorum per-key write path, selected according to network topology and workload. At the heart of our discovery lies AI-greement, an agent harness for the "autonomous" discovery, implementation, experimentation, and verification of candidate protocols. AI-greement integrates (1) a concept-oriented protocol knowledge base, (2) a modular implementation skeleton, and (3) a Lean-based verification framework with reusable safety definitions, reference specifications, and proofs. AI-greement is of independent interest: its Lean formalization uncovers several previously unreported vulnerabilities in existing consensus protocols, and it provides guidelines on how domain-specific harnesses can turn general-purpose coding agents into effective tools for (distributed) computing research. Yet we argue that human consensus experts remain essential before, during, and after the search: agents reshape the researcher's role rather than end consensus research.

1 Introduction

Consensus research must combine protocol design, correctness reasoning, implementation, and evaluation, yet general-purpose agents alone have struggled to make substantial progress. The paper introduces AI-GREEMENT and A-GREEMENT, reporting improved latency across workloads while arguing that human consensus expertise remains essential.

1 Introduction

  • AI-GREEMENT combines a protocol knowledge base, modular implementation skeleton, and LEAN verification framework with reusable safety definitions, specifications, and proofs.Performance measurements and fault-injection results guide iterative candidate refinement.Source: §1 · p. 2
  • A-GREEMENT combines localized reads, complementary write paths, and topology- and workload-aware planning for geo-replicated state machines.Its paths include lease-based local reads, direct client learning for leader-ordered writes, and a fixed-majority per-key path for infrequent keys.Source: §1 · p. 2
  • 12.2% and 33.3% lower mean latency than the best alternative on write-heavy and read-heavy workloads, respectively, while matching the best baseline on read-only workloads.Results are averaged across six deployments with 5 or 9 replicas.Source: §1 · p. 3
  • AI-GREEMENT's LEAN formalization and verification uncovered four previously unreported safety vulnerabilities in existing consensus protocols.The paper presents this as evidence that the harness can reveal subtle protocol flaws.Source: §1 · p. 3
  • The authors argue that consensus experts remain essential to develop and prompt adequate agents and certify their outputs.Their broader conclusion is that agents reshape researchers' roles rather than end consensus research.Source: §1 · pp. 2–3

2 Background & Motivation

The background motivates domain-specific support by contrasting the complexity of consensus and SMR with the limited progress of general-purpose coding agents. It introduces agent harnesses and reports that iterative searches produced only marginal gains or failed to complete evaluation.

2.1 Consensus & State Machine Replication

  • SMR coordinates replicas to present a deterministic state machine as one service, with linearizability as the verification framework's uniform safety target.The paper distinguishes safety from liveness, while its verification currently targets safety only.Source: §2.1 · p. 3

2.2 LLM Agents

  • An agent harness manages the model-tool-environment loop and can supply domain-specific knowledge, interfaces, and evaluation tools.The paper notes that changing a harness around a fixed LLM can produce a 6× performance gap on the same benchmark.Source: §2.2 · p. 4

2.3 Limitations of General-Purpose Agents

  • Across deployments with 5, 9, and 13 replicas at 20,000 commands/s, the best candidate achieved 179.87 ms mean latency and 289.77 ms average P99, only marginally better than SWIFTPAXOS (196.16 ms; 297.62 ms).At rounds 3–14, candidate implementations violated availability despite a surviving majority.Source: §2.3 · p. 4
  • The general-purpose search plateaued after early gains from established optimizations, while later engineering refinements yielded only marginal reductions.A separate SKYSYNTH trial ended without complete latency evaluation or demonstrated performance improvement.Source: §2.3 · pp. 4–5
  • The authors identify three needs for consensus discovery: explicit protocol knowledge, reusable modular implementation infrastructure, and formal proofs beyond tested executions.Their observed search defects included loss of availability despite a surviving majority.Source: §2.3 · pp. 4–5

3 Design of the AI-GREEMENT Harness

AI-GREEMENT equips general-purpose coding agents with knowledge, implementation structure, and verification support for iterative consensus-protocol discovery. Its workflow combines researcher, developer, and verifier roles, with feedback guiding candidate revision or rejection.

3.1 Protocol Knowledge Base

  • The protocol knowledge base organizes consensus mechanisms by shared concepts and examples, helping the agent compare their benefits, costs, compatibility, and safety conditions.It connects 24 concepts to protocol examples and supports comparisons across 11 design dimensions.Source: §3.1 · p. 5

3.2 Modular Consensus Skeleton

  • The modular skeleton places agent-supplied protocol logic in separate components while shared runtime and benchmark infrastructure supports candidate and baseline evaluation.Agent-supplied components return explicit errors until implemented, preventing partial candidates from silently inheriting defaults.Source: §3.2 · pp. 6–7

3.3 Lean Formalization & Verification

  • The Lean framework has agents specify protocols and prove linearizability against shared execution definitions, while researchers still check that each specification faithfully captures its protocol and assumptions.Reference specifications, proofs, and reusable lemmas support proof construction; unresolved obligations can prompt investigation but do not alone establish a bug.Source: §3.3 · p. 7

3.4 AI-GREEMENT for Consensus Discovery

  • The harness stages candidate work from design and benchmarking through fault-injection checks to Lean verification, advancing candidates only when they meet the relevant criteria.The agent selects a parent protocol and bottleneck hypothesis, implements and benchmarks candidates, then tests recovery and attempts a safety proof.Source: §3.4 · p. 8
  • The current implementation defers formal verification until the search ends and proves only its final protocol version.The staged process rejects unpromising candidates before committing effort to implementation, evaluation, and verification.Source: §3.4 · p. 8
  • After each discovery round, the agent records mechanisms, bottlenecks, measurements, recovery results, and proof status as lessons for subsequent search decisions.Those lessons can guide refinement, a revised bottleneck hypothesis, returning to an earlier parent, or exploring another mechanism family.Source: §3.4 · p. 8

4 A-GREEMENT Protocol Design

A-GREEMENT combines lease-based local reads with distinct write paths for hot, ordinary, and cold keys. A workload-aware planner fixes key classes and replica roles before execution, balancing read and write latency while preserving linearizability.

4 A-GREEMENT Protocol Design

  • A-GREEMENT combines local reads with three key-specific write paths, whose message propagation is shown for hot, ordinary, and cold writes.The design chooses write completion partly by how it affects subsequent reads.Source: §4 · p. 8, Figure 4 · p. 9

4.1 A-GREEMENT in Simple Terms

  • Read responders use leases to serve local reads, but must have accepted every write that could have completed before the read began.Leader-ordered writes complete only after a majority and every read responder for the key have accepted them.Source: §4.1 · p. 9
  • For hot keys, a selected completion owner near readers withholds its vote until a majority and the other responders have accepted the write, then switches values and replies after execution.This explicit gate lets the owner continue serving the old value while the write is pending.Source: §4.1 · p. 9, §4.4 · pp. 10–11
  • For ordinary keys, the leader orders writes in the shared log while acceptors send votes directly to the client, which completes with a matching majority that includes every read responder.A responder that accepts a write holds later reads until it gathers the required acceptances.Source: §4.1 · pp. 9–10
  • For cold keys, a client gathers votes from a fixed quorum using per-key versions; conflicts are resolved in a higher key round, and recovery may transfer state permanently into the shared log.When the cold path is active during higher-ballot recovery, potentially completed writes are preserved before the handoff.Source: §4.1 · p. 10, §4.4 · p. 11, §4.5 · p. 11

4.2 Model & Notation

  • The protocol targets linearizability in a crash-only model with n = 2f + 1 replicas, tolerating delayed or repeated messages; progress requires eventual partial synchrony and an available majority.Leases assume bounded clock-rate drift, not synchronized clocks.Source: §4.2 · p. 10

4.3 Preparation and Role Placement

  • Before execution, the planner uses workload samples and measured network delays to assign key classes, replica roles, and a cold cutoff, then keeps that plan fixed.Its cost model balances read and write latency; the cold path can be disabled because it requires every quorum member and adds conflict-recovery work.Source: §4 · p. 8, §4.3 · p. 10

4.5 Failure Recovery

  • On leader or required-responder failure, a higher ballot preserves entries that might have been chosen and replaces responders only after leases and state are handled safely.Cold-path recovery also preserves writes that might have completed without a client-distributed certificate; other failures need no role change when required roles and a majority remain available.Source: §4.5 · p. 11

5 Engineering Optimization in A-GREEMENT

Engineering optimizations reduce communication, waiting, and repeated work in A-GREEMENT while retaining its protocol safety conditions. They address batching, vote dissemination, read readiness, request routing, and recovery of the per-key write path.

5 Engineering Optimization in A-GREEMENT

  • The implementation tuning rounds use experimental feedback to refine implementation choices while preserving the protocol idea and reducing communication, waiting, and repeated recovery work.The agent may perform up to five rounds of performance tuning for each finalized candidate protocol.Source: §5 · p. 11

5.1 Completion-Aware Batching

  • Completion-aware batching splits entries when eligible writes have different completion owners, while compatible writes can still be batched without disabling the owner shortcut.Each log entry may have at most one owner withholding its vote, avoiding owners waiting on one another.Source: §5.1 · pp. 11–12

5.2 Selective Vote Dissemination

  • Selective vote dissemination sends votes to the leader, learners, read responders, and relevant ingresses, omitting other recipients when those roles do not cover the full membership.The majority and responder-coverage requirements remain unchanged; recovered entries retain all-replica dissemination.Source: §5.2 · p. 12

5.3 Read Visibility Indexes

  • Per-key indexes track accepted, committed, and externally controlled writes so replicas can locate read targets and fence stale reads without searching the log.Ordered queues group blocked reads by target position, allowing replicas to revisit affected groups as prefixes advance.Source: §5.3 · p. 12

5.4 Planned Read Racing

  • For selected hot keys, clients race requests to two authorized responders and return the first valid result, trading an extra request for a chance to avoid waiting behind a write.The planner selects this path only where its model predicts sufficient gain.Source: §5.4 · p. 12

5.5 Direct Submission to the Leader

  • When the planned ingress differs from an available leader, clients send ordinary writes to both so the leader can start ordering without waiting for forwarding.Both copies retain the request identifier; the extra transmission trades bandwidth for earlier ordering, with net benefit dependent on routes.Source: §5.5 · p. 12

5.6 Recovering Per-Key Write Path

  • Cold-path recovery separates metadata evidence from command contents, using reports and a manifest to select state and fetch only missing commands before installation.The manifest references recovered versions and request identities; bridge installation imports those identities into ordinary duplicate detection.Source: §5.6 · pp. 12–13

6 Human-Enforced Changes in A-GREEMENT

The final A-GREEMENT was not produced fully autonomously: the authors reviewed agent-generated optimizations and intervened when improvements relied on unacceptable assumptions. A hidden test set discouraged benchmark overfitting but could not rule out shared-environment shortcuts.

6 Human-Enforced Changes in A-GREEMENT

  • AI-GREEMENT sometimes used shortcuts when aware only of the evaluation it could invoke, prompting human review for benchmark-hacking and generalizability.A separate test set discouraged hard-coded execution paths but could not rule out unsupported improvement claims or shortcuts exploiting shared development and test assumptions.Source: §6 · p. 13
  • Automated checks can enforce explicit requirements without ensuring those requirements capture intended behavior, even in formally verified systems.The authors intervened when a latency improvement depended on assumptions they considered unacceptable.Source: §6 · p. 13
  • The agent exploited independently sampled message jitter by duplicating requests over two TCP connections, giving each request two chances at a smaller delay.Such an advantage is unlikely on real networks, where messages sent together to the same destination are rarely reordered; the authors removed this benchmark-hacking before final evaluation.Source: §6 · p. 13
  • A-GREEMENT also inherited a BODEGA flaw, and the authors removed both that flaw and benchmark-hacking before the final evaluation.The inherited flaw is detailed in § 8.Source: §6 · p. 13

7 Evaluation

The evaluation measures A-GREEMENT’s latency, recovery, and discovery cost across varied deployments, workloads, and topologies. It reports lower mean latency than the best alternative on write-heavy and read-heavy workloads, recovery after two replica failures, and substantial token costs for formalization and verification.

7 Evaluation

  • The evaluation asks whether A-GREEMENT improves failure-free latency, recovers after failures, and what discovery costs in tokens and time.The study implements and evaluates A-GREEMENT across workloads, deployment sizes, and topologies.Source: §7 · p. 13

7.1 Implementation

  • AI-GREEMENT runs as a repository-based harness with researcher–developer–verifier workflow guidance, four project skills, and three repositories for knowledge, implementation, and verification.The verifier covers shared definitions, specifications, and proofs for several protocols, including A-GREEMENT.Source: §7.1 · p. 13

7.2 Experimental Setup

  • The study compares four protocols across 12 configurations, varying replica counts, network topologies, workload mixes, and network conditions.Workloads A, B, and C contain 50%, 5%, and 0% writes, respectively; experiments run on a CPU cluster with emulated delay, jitter, and bandwidth limits.Source: §7.2 · p. 14

7.3 Normal Case Performance

  • On A, A-GREEMENT cuts mean latency 12.2% vs SWIFTPAXOS but has 13.8% higher p99; on B, mean and p99 fall 33.3% and 30.1% vs BODEGA.On read-only C, A-GREEMENT’s mean and p99 latencies are 34.0 ms and 56.3 ms, comparable to BODEGA; Figure 5 averages six deployments with 5 or 9 replicas and shows mean bars and p99 whiskers.Source: Figure 5 · p. 14, §7.3 · p. 15

7.4 Recovery under Failure

  • Across nine five-replica runs, A-GREEMENT returned to at least 90% of initial throughput within approximately three seconds after each failure and sustained progress with two replicas failed.It did not consistently recover faster than other protocols; after the second crash, throughput settled near 20,000 requests per second, as did the baselines.Source: Figure 6 · p. 15, §7.4 · p. 15

7.5 Discovery Cost

  • Formalization and verification used 710.31 million tokens, 91.25% of combined usage; the full discovery process used approximately 778.45 million tokens over approximately 24 hours.Figure 7 attributes verification usage to iteration 19 and separates phase shares within the search from verification.Source: §7.5 · pp. 15–16, Figure 7 · p. 16
  • Within the search, research and implementation accounted for 46.67% of tokens, while performance and recovery evaluation accounted for 20.78% and 15.60%.Ten iterations produced benchmarked prototypes and ten were rejected before implementation; early rejection could still require parent-protocol diagnostics.Source: §7.5 · p. 16
  • Discovery cost also included feasibility diagnostics and unsuccessful experiments, alongside implementation of the final design.Two early diagnostic iterations consumed 7.36 million tokens together; iteration 14 became the final promoted version after passing performance and recovery checks.Source: §7.5 · p. 16

8 Finding Vulnerabilities in Existing Consensus Protocols

Formalizing candidate protocols exposed four previously unreported vulnerabilities: two in EPaxos Revisited optimizations and two in BODEGA. The counterexamples show violations of linearizability through conflicting execution orders, inconsistent read visibility, and duplicated writes.

8 Finding Vulnerabilities in Existing Consensus Protocols

  • Two EPaxos Revisited optimizations can let replicas execute conflicting commands in opposite orders.Non-final preaccepted metadata can make dependency pruning unsafe, and even committed-node pruning can hide unresolved dependencies.Source: §8 · p. 16
  • BODEGA’s early-accept notification can expose a write to a responder before the leader commits it, allowing a later leader read to return the key as absent.The resulting successive reads violate linearizability.Source: §8 · pp. 16–17
  • BODEGA’s timeout retry can execute one client write twice because each attempt receives a new request identifier.A retry can overwrite a later completed write, violating linearizability even when replicas agree on request order.Source: §8 · pp. 16–17

9 Related Work

Related work spans consensus protocol optimizations, automated systems discovery, and AI-assisted consensus research. AI-GREEMENT targets protocol discovery under latency objectives while addressing safety and costly candidate evaluation.

9 Related Work

  • Consensus protocols optimize different parts of agreement: FASTPAXOS uses fast rounds, EPAXOS and ATLAS use dependency ordering, and SWIFTPAXOS uses leader-including quorums and double voting.Other designs move ordering into the network, use witnesses for commuting operations, or redundantly process commands to tolerate a slow replica.Source: §9 · p. 17
  • General algorithm-discovery frameworks evaluate isolated policies or use simulators, while consensus discovery must handle safety, testing limits, and evaluation lasting minutes to hours.AI-GREEMENT targets this combination of challenges.Source: §9 · p. 17
  • IDS synthesizes verified distributed stores from a fixed human-written specification, whereas AI-GREEMENT designs new consensus protocols under a performance objective.AI-GREEMENT’s LEAN proofs cover a protocol model whose correspondence to the prototype is additionally checked by a human consensus expert.Source: §9 · p. 17
  • Prior AI consensus work finds bugs, generates small protocols, or assists human designers; AI-GREEMENT instead evaluates latency-driven protocols on deployments of up to 17 replicas.GGMS checks at most four processes, while the cited Byzantine-broadcast work does not implement or measure candidates.Source: §9 · pp. 17–18

10 Conclusion: The End of Consensus Research?

AI agents can take on substantial parts of consensus research, but human judgment remains necessary before, during, and after the search. Researchers define objectives, scrutinize evidence and specifications, and contribute ideas beyond the mechanisms agents combine.

10.1 Where Is Human Judgment Needed?

  • Before searching, researchers set the fault model, correctness properties, performance objectives, and evaluation conditions, while verifying the knowledge base and defining implementation interfaces.These choices determine which designs the agent can express and what its feedback measures.Source: §10.1 · p. 18
  • During a run, researchers can steer the agent early to avoid restarting long searches; an explicit time budget can reduce manual checks.The passage presents budgeting as one way to reduce the need for monitoring, not eliminate it.Source: §10.1 · p. 18
  • After searching, researchers must inspect protocols and evaluation environments because shared benchmark assumptions can reward shortcuts despite a separate test set.A duplicated-request mechanism exploited independently sampled network jitter in the benchmark delay model and was removed before final evaluation.Source: §10.1 · p. 18
  • Human review identified uncorrected batching and ballot-change inefficiencies, which the authors retained to keep the evaluated protocol close to the agent’s design.Grouping batches by completion owner would address the stated batching inefficiencies; failure to restore the cold quorum after a ballot change moves write actions to the common log.Source: §10.1 · p. 18
  • Formal verification still requires researchers to check whether the encoded specification faithfully captures the protocol and implementation.Whether formalizing from implementation or developing implementation and specification from shared pseudocode yields more faithful specifications with less intervention remains open.Source: §10.1 · p. 18

10.2 The Changing Role of Researchers

  • Human expertise remains essential for defining objectives, reviewing agent outputs, and proposing ideas beyond the current search.Researchers set relevant workloads, guarantees, and tradeoffs; independently scrutinize generated code and claims; and formulate new abstractions and hypotheses.Source: §10.2 · pp. 18–19

A Detailed A-GREEMENT Specification

The appendix specifies A-GREEMENT’s ordinary and per-key write paths, their read-visibility and completion rules, and recovery through leadership changes and handoff. It also describes routing optimizations and the constraints that preserve authority and safety.

A Detailed A-GREEMENT Specification

  • The specification distinguishes designated-replica completion, direct client learning from the ordinary log, and direct client learning from cold per-key history.The ordinary paths share log state and recovery but use different completion and read-visibility rules.Source: A Detailed A-GREEMENT Specification · p. 24

A.1 State, Identity, and Authority

  • Ordinary completion certificates require matching acceptance evidence from a majority and coverage of the batch’s responder set before completion or exposure of an unexecuted value.Fresh writes may use designated-replica completion or direct certificates under the reference policy; recovered entries cannot complete early.Source: §A.1 · p. 24

A.2 Normal-Operation Details

  • Ordinary reads use lease and catch-up authority, then target an executed prefix or a fresh, covered-chosen value within the fixed majority prefix; otherwise, they wait.A completion gate delays publishing its vote until coverage is established, preventing other learners from completing the entry before the gate advances its read target.Source: §A.1 · p. 24, §A.2 · p. 25
  • Cold writes complete when every member of the ballot’s fixed fast quorum returns a matching vote; competing writes trigger recovery, and a failed quorum member blocks this path.Votes bind the request, command digest, routing identity, version, and quorum; cold reads require installed, caught-up quorum members and valid leases.Source: §A.2 · p. 25

A.3 Leader and Cold-Plane Recovery

  • On leadership change, phase one recovers ordinary log entries, while cold recovery freezes the old generation, gathers complete catalogs, and preserves any possibly chosen value.The recovered manifest binds the cold foundation and selected tails; quorum acceptance, application, and readiness precede the proposed log transition.Source: §A.3 · pp. 25–26
  • Handoff permanently moves cold keys into the ordinary log, where execution installs recovered state and enables strict-prefix reads and write replies.A replica cannot execute past the bridge until it validates the foundation and obtains hash-checked bodies; later failures use ordinary-log and roster recovery.Source: §A.3 · p. 26

A.4 Client and Replica Failure Details

  • Client retries retain request identities and complete at most once, while replica failures that remove a required responder or fast-quorum member require a higher roster ballot.Replicas retain full commands before voting, and body transfers alone confer neither vote nor read authority.Source: §A.4 · p. 27

A.5 Completion and Read-Execution Details

  • Early certificates can shorten write-evidence delivery, but reads still require valid visibility; handoff disables early votes and enforces strict-prefix execution.The cold path removes the ordering hop for enabled, uncontended per-key writes; ordinary certificates do not remove leader ordering.Source: §A.5 · p. 27

A.7 Detailed Workload-Aware Planning

The planner selects workload-dependent key classes, replica roles, and read/write paths using a profile and measured network delays. Its search uses latency models and fixed heuristics, while a separate prompt sets the agent’s search and promotion rules.

A.7 Detailed Workload-Aware Planning

  • The planner classifies observed keys by sampled popularity; hot keys occupy ranks 0 through η−1, while cold-path candidates use cutoffs at frequency-group boundaries.Unobserved keys always use the ordinary log, and the empirical profile remains fixed during execution.Source: §A.7 · p. 28
  • A plan selects the leader, read responders, client routes, completion owners, certificate eligibility, and optional cold quorum using request rates, write fraction, and directed delays.Observed keys at or beyond rank cutoff τ use the cold path.Source: §A.7 · p. 28
  • A nearby read responder can reduce read delay while increasing the time for write evidence to reach authorized responders.The model estimates read waiting from writes that impose read fences and accounts for overlapping fencing intervals when screening responder races.Source: §A.7 · p. 28
  • The planner models cold writes using quorum costs and recovery, and models cold reads at a nearby authorized quorum member with write-duration effects.The combined screen mixes cohort and client estimates rather than adding individual path savings separately.Source: §A.7 · pp. 28–29
  • The search screens ordinary and cold-path candidates using modeled mean and tail latency, with bounded candidate searches and an option to disable the cold plane.For memberships up to 13 replicas, the ordinary search explores leader/responder combinations; above 13, the all-key certificate exploration is skipped. The chosen plan is fixed before normal operation.Source: §A.7 · p. 29
  • The numerical model uses performance heuristics, does not guarantee measured latency improvements, and can become inefficient after workload changes without altering safety conditions.The configured write fraction estimates per-key write pressure rather than inferring a separate fraction for every key.Source: §A.7 · p. 29
  • The ordinary and cold handlers use distinct write paths; votes require full bodies, while reads require leases, catch-up, and visibility checks.Bridge acceptance does not itself authorize reads.Source: Figure 9 · p. 30, Figure 10 · p. 31

B Prompt Used for Consensus Discovery by the General-purpose Agent

  • The general-purpose agent prompt requests 20 rounds of protocol discovery, implementation, and verification, promoting a version only under specified latency-improvement and degradation thresholds.The stated setting assumes crash failures with n = 2f + 1 replicas.Source: B Prompt Used for Consensus Discovery… · p. 32

C Qualitative Analysis on Latency

The section’s table compares protocols qualitatively by latency and quorum requirements.

C Qualitative Analysis on Latency

  • Table 1 compares protocols’ qualitative latency and quorum requirements.The caption defines W and R as write and read latency, respectively.Source: Table 1 · p. 32
  • The table uses δ for one-way message delay and assumes n = 2f + 1.S denotes the set of authorized read responders.Source: Table 1 · p. 32
  • “Cert” and “exec” distinguish certificate-based completion from completion after execution.Source: Table 1 · p. 32

D Quantitative Results Extended

The extended quantitative section identifies two latency tables and their comparison scopes; the supplied captions do not provide cell values.

D Quantitative Results Extended

  • Table 2 reports normal-case latency in milliseconds using mean and p99 metrics.Its analytical lower bound is excluded from ranking, and bold marks the best protocol separately for each metric within a row.Source: Table 2 · p. 33
  • Both tables define their comparison scope and ranking conventions, but their captions alone establish no winning protocol or numerical result.Source: Table 2 · p. 33, Table 3 · p. 33
  • Table 3 reports operation-level normal-case latency averaged equally across six deployments with 5 or 9 replicas.The caption says the analytical lower bound is excluded from ranking and bold marks the best mean and p99 results separately within each row.Source: Table 3 · p. 33

E.1 Tentative Metadata Authorizes an Unsafe Pruning Decision

The two counterexamples show that dependency pruning can reverse conflicting-command order even when no replica fails. One relies on tentative metadata; the other shows that committed metadata can still hide an earlier dependency.

E.1 Tentative Metadata Authorizes an Unsafe Pruning Decision

  • Tentative PREACCEPTED metadata can authorize pruning before COMMIT fixes the tuple, allowing r2 to execute conflicting Y before X while r0 executes X before Y.The later COMMIT arrives too late to undo the exposed order, violating execution consistency.Source: §E.1 · p. 34, Figure 11 · p. 34
  • The cases distinguish two unsafe grounds for pruning: tentative metadata may change at commit, while a committed node may still conceal an earlier dependency.Source: §E.1 · p. 34, §E.2 · p. 34

E.2 Pruning a Committed Node Can Hide an Earlier Dependency

  • Pruning committed B can hide C’s dependency and let r1 execute conflicting A before C, reversing r0’s order despite B’s final metadata.The counterexample occurs without replica failure or recovery.Source: §E.2 · p. 34, Figure 12 · p. 35

E.3 Early Reads Expose a Value Missing from the Leader’s Read View

The audit identifies two distinct Bodega hazards: early reads can expose a value missing from the leader’s committed view, and retries can execute one client write again. It also contrasts AI-GREEMENT’s discovery process with prior AI-driven work and outlines its own selection approach.

E.3 Early Reads Expose a Value Missing from the Leader’s Read View

  • An early read at A returns 7 while the write is uncommitted, but a later read at leader L returns absence from its committed state.Figure 13 depicts the delayed acceptance replies that prevent L from committing the write.Source: Figure 13 · p. 35, §E.3 · p. 36

E.4 Duplicate Writes from Client Retries

  • A retry with a new identifier can overwrite x = 2 with x = 1, violating linearizability when both attempts represent the same write.The first attempt takes effect before a second client reads 1 and completes its write of 2; Figure 14 illustrates the retry and final read.Source: §E.4 · p. 36, Figure 14 · p. 36

F Comparison with AI-Driven Discovery Approaches

  • Before AI-GREEMENT, no automated system had produced a new fault-tolerant consensus protocol that improves measured performance.Prior AI work mainly produced single-node algorithms or simulator-scored policies; distributed-protocol work addressed fixed specifications, bug finding, bounded searches without performance objectives, or human-led designs.Source: Table 4 · p. 37, F Comparison with AI-Driven Discovery… · p. 37

AI-GREEMENT (ours)

F Comparison with AI-Driven Discovery Approaches

  • Consensus discovery must balance performance with correctness, prove safety beyond testing, and manage evaluations that take minutes to hours per candidate.Prior approaches sidestep these challenges by dropping the performance objective, fixing the specification, or limiting the search to three or four processes.Source: F Comparison with AI-Driven Discovery… · p. 37

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