Fast Tendermint: Speeding Up a Foundational Consensus Protocol

Daniel Cason; Preston Vander Vos

REVIEW 2 major objections 6 minor 12 references

Fast Tendermint: Speeding Up a Foundational Consensus Protocol

T0 review · 2 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A two-step variant of Tendermint for networks with fewer faults

desk verdict A clean and honest two-step Tendermint variant for n>5f with plausible safety proofs, but the termination argument has a real gap and the model-checking claim is underspecified. read the letter →

arxiv 2608.13434 v1 pith:U6XBQ6N7 submitted 2026-08-13 cs.DC

Preston Vander Vos , Daniel Cason This is my paper · ORCID

classification cs.DC MSC 68M1468M1568M20

keywords BFTconsensusTendermintpartialsynchronygood-caselatencyByzantinefaultsleaderrotationQuintspecificationprotocol

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that a lightly modified Tendermint consensus protocol can decide in two communication steps, not three, by assuming a stricter fault budget of $n > 5f$ instead of the usual $n > 3f$. The key move is to drop the prevote round entirely and let a single round of precommits, together with the proposal, determine the decision. A sympathetic reader would care because Tendermint is already widely deployed in blockchains, and a shorter good-case latency translates directly to faster finality without abandoning Tendermint's simple, per-round leader rotation.

What carries the argument

The central object is the merged valid state $(round, value)$ that a process updates only after observing $2f+1$ precommits for a value in a round, plus the observation rule and re-proposal rule that carry safety across rounds. This machinery replaces Tendermint's separate locked and valid variables and its two-step voting pipeline, making a single precommit step sufficient to decide when the proposer is correct and the network is synchronous.

What would settle it

A concrete counterexample would be a schedule of adaptive timeouts and a round sequence in which, after GST, every round with a correct proposer has one of the timing conditions of Lemma 6 violated (e.g., timeoutPropose(r) not exceeding 2∆ + timeoutPrecommit(r) or timeoutPrecommit(r) not exceeding 2∆), so that no round ever yields a decision, showing termination fails.

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Extended reading notes

Core claim

The paper introduces Fast Tendermint, which preserves Tendermint's leader-rotation structure while merging the locked and valid state variables into a single valid pair, and collapsing the prevote and precommit steps into one voting step. In the good case, a correct proposer broadcasts a proposal and processes decide once they have the proposal and $n-f$ matching precommits for a value. The paper proves Agreement, Validity, and Termination in the partially synchronous model with the gossip property, relying on the observation that any $n-f$ quorum and any $2f+1$ quorum of precommits must intersect in a correct process when $n > 5f$.

Load-bearing premise

The termination proof assumes that after the network stabilizes, a round eventually starts with a correct proposer while the adaptive timeout values satisfy the timing inequalities of Lemma 6, but the paper asserts this without proving that such a round exists.

Editorial extensions

If this is right

Fast Tendermint shows that an existing, production-grade consensus protocol can be adapted to the $n > 5f$ setting without introducing complex view-change machinery, potentially lowering the barrier to adopting faster finality in blockchains.
If correct, the protocol inherits the two-step good-case latency of other $n > 5f$ protocols while maintaining Tendermint's simple round-based leader rotation, which could make it easier to deploy in existing Tendermint-based systems.
The proof that a single precommit round suffices relies on the quorum intersection $n-f$ and $2f+1$ overlapping in a correct process, a property that holds exactly when $n > 5f$, so the protocol does not extend to the tighter $n \geq 5f-1$ bound without additional mechanisms.
The paper's formal specification in Quint, model-checked, provides a machine-checkable artifact that can be reused for future modifications to the protocol.
The protocol's slow path remains simple but nontrivial: when the proposer is faulty or the network is asynchronous, processes fall back to multi-round operation controlled by adaptive timeouts, preserving termination at the cost of latency.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural next step is to determine whether a fast path with $n > 5f$ can be combined with a failure-optimal slow path that still tolerates $f < n/3$, an open question the paper itself notes; the current protocol gives up the larger fault budget on the slow path.
The proof of termination rests on an assumption about adaptive timeouts and round rotation after GST, so a concrete implementation would need to specify timeout growth to make the termination guarantee unconditional.
The two-step good-case latency of Fast Tendermint could plausibly be measured against Tendermint's current latency in a testbed, providing an experimental check on how much of the theoretical speedup survives in real network conditions.
The paper's decision rule, which triggers on the proposal plus $n-f$ precommits regardless of the receiver's current round, is a distinctive mechanism worth comparing with the decision rules of other $n > 5f$ protocols to see whether it yields a simpler liveness proof.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things about this paper. First, the core contribution is real: it takes Tendermint, drops the prevote step, merges locked and valid, and gets two-step good-case finality under n>5f while keeping the per-round leader rotation. Second, the safety side is in decent shape, but the liveness proof is not. The termination theorem is asserted, not derived.

What the paper does well: the adaptation is minimal and clearly presented. The counting arguments in Lemma 2 and Theorem 3 are careful and consistent with the n>5f threshold. The validity proof is clean. The authors also situate the work honestly in the literature, crediting FaB Paxos, Minimmit, BlueBottle, and the 5f-1 tight bound. They ship a Quint specification, which is a real artifact.

The soft spots are proportionate. The load-bearing one is the termination gap. Lemma 6 assumes all correct processes enter round r within Delta of the first correct process. That does not follow from the gossip property given the protocol's only round-advance path: the quorum-any rule schedules a timeout for a future round, and a process that is several rounds behind at GST can stay behind forever if adaptive timeouts keep growing. Theorem 7's claim that eventually a round satisfies the lemma's conditions is exactly the missing lemma. This is not a minor stylistic issue; without it termination is unproven. Second, the decision rule in line 36 uses r' without binding it to the proposal round r. The prose says "matching" precommits, but the pseudocode should be explicit that r'=r. That is minor but confusing. Third, the Quint model-checking claim is vague: no details on instance sizes, what properties were checked, or how far the check went. Since model checking cannot establish unbounded termination, this doesn't fix the gap.

The reader's conditional verdict is fair, and the stress-test note correctly identifies the weakest point. This paper is for the BFT consensus community, particularly people working on low-latency blockchains who want a minimal modification of a deployed protocol. It deserves a serious referee, but the termination proof needs a real liveness lemma, and the pseudocode needs cleaning up before it is acceptable.

Referee Report

2 major / 6 minor

Summary. The paper presents Fast Tendermint, a modification of the Tendermint BFT consensus protocol for systems with n > 5f Byzantine processes. The main idea is to collapse Tendermint's prevote and precommit steps into a single PRECOMMIT step and to merge the locked and valid state variables, which yields two communication steps in the good case (propose, then precommit). The paper claims Agreement, Validity, and Termination in the partially synchronous model with a gossip communication property, and it accompanies these claims with hand-written proofs and a Quint/TLA+ specification used for model checking.

Significance. If the result is correct, the paper makes a useful contribution: it shows that a relatively small modification of a widely deployed consensus protocol can achieve two-step good-case latency under the n > 5f fault-tolerance assumption, while retaining Tendermint's round-rotation mechanism. The safety proofs are careful and the counting arguments are consistent with the n > 5f threshold. The paper also provides a formal specification in Quint, which is a concrete asset. However, the termination proof is currently a sketch rather than a rigorous derivation, and the adaptive timeout schedule on which liveness depends is not specified. Since Termination is one of the three central claimed properties, this gap is load-bearing and must be addressed before the paper can be accepted.

major comments (2)

[§4, Theorem 7] Termination is asserted rather than proved. Theorem 7 states that after GST there is guaranteed to be a round r satisfying Lemma 6, with a correct proposer and with t > GST + timeoutPrecommit(r−1), timeoutPropose(r) > 2Δ + timeoutPrecommit(r), and timeoutPrecommit(r) > 2Δ, but no argument is given that the protocol's round progression actually reaches such a round. The adaptive timeout schedule is never defined, and the statement that timeouts "increase over rounds" does not by itself show that a round satisfying all of Lemma 6's conditions eventually occurs. In particular, condition (1) requires the round to start after GST plus the previous round's precommit timeout, and the proof must show that the waiting time for round r eventually exceeds this bound. Because Termination is one of the three stated properties, this gap is load-bearing for the paper's main claim.
[§4, Lemma 6] Lemma 6's proof assumes without derivation that every correct process enters round r within Δ of the first correct process. This conclusion is not automatic: the first correct process enters r because its timeoutPrecommit(r−1) expired after it received an n−f precommit quorum for round r−1, but that quorum may contain Byzantine-signed messages that were received by only a subset of correct processes. The proof must explicitly use the second clause of the gossip property, which propagates any message received by a correct process, to show that every correct process receives the same quorum and therefore schedules the same timeout and enters round r by t+Δ. Lemma 5's proof has the same unstated propagation step when it infers that all correct processes schedule the timeout at most Δ after proposer p. These steps are likely fixable, but as written they are a gap in the derivation of Lemma 6 and hence in the liveness argument.

minor comments (6)

[Algorithm 1, line 36] The decision rule pairs a fresh proposal for round r with n−f precommits for a value from an arbitrary round r′, without stating the relationship between r and r′. The proof of Theorem 3 refers to "the round rp" of the precommits, so the pseudocode should say explicitly that safety holds for any r′ and that the proposal round is not used in the agreement argument.
[§2 and §4] The functions timeoutPropose(r) and timeoutPrecommit(r) are never defined. A concrete adaptive schedule is needed for the termination proof to be verifiable; for example, the paper could specify a deterministic increasing function of the round number and prove that the timing conditions of Lemma 6 are eventually satisfied.
[§1 and §4] The claim that the protocol was model-checked in Quint would be more informative if the paper reported the parameters checked, such as the values of n and f, the number of rounds explored, and the properties verified.
[§4, Lemma 1] The phrasing "Any two sets of n−f and 2f+1 processes" should be "Any two sets of size n−f and 2f+1 processes" for clarity.
[§4, Lemma 5] In the sentence "Since p scheduled it after GST", the pronoun "it" is ambiguous; it should read "Since p scheduled timeoutPrecommit(r−1) after GST".
[§4, Lemma 6] The phrase "all n−f correct precommits" is imprecise; there are n−f correct processes in the good case, and the proof should say that the n−f precommits broadcast by those processes are received by all correct processes within 2Δ, using the gossip property applied to each send.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Fast Tendermint's claims are derived from its protocol assumptions and internal proofs, with no fitted inputs or self-citation chain.

full rationale

The derivation chain is self-contained. The protocol fixes n > 5f and defines valid values through 2f+1 precommits; Lemmas 1-6 and Theorems 3-4 prove agreement and validity from quorum intersection, and the decision rule is independent of the assumptions. No parameter is fitted to data, no prediction is renamed from an input, and the only self-citations (e.g., [26] BlueBottle, [7] Tendermint performance) are contextual related-work references, not load-bearing justifications for Fast Tendermint's safety or liveness. The termination proof (Theorem 7) does contain a genuine gap - it asserts rather than proves that a round satisfying Lemma 6's conditions eventually occurs - but this is a missing liveness argument, not circularity: Lemma 6's conditions are not equivalent to the theorem's conclusion, and no quoted step reduces the target claim to its own input. Accordingly the circularity score is 0.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The protocol rests on the standard partially synchronous model with gossip communication, PKI and signed messages, collision-resistant identifiers, n > 5f, and an application-specific validate() predicate. No numeric parameters are fitted to data and no new entities are introduced.

assumptions (6)

domain assumption Partially synchronous model with a global stabilization time (GST) and bound Δ such that every message sent after GST is delivered within Δ.
Stated in Section 2 as the system model inherited from DLS; used in Lemmas 5 and 6 for the liveness timing bounds.
domain assumption Gossip communication property: any message sent or received by a correct process is eventually received by all correct processes within Δ of max{time, GST}.
Stated in Section 2; load-bearing for Lemma 5 and Lemma 6 because it lets the proposer learn all valid updates and lets all processes receive the proposal and precommits in bounded time.
domain assumption Public-key infrastructure with signed messages; correct processes only accept messages with valid signatures and each correct process sends at most one precommit per round.
Stated in Section 2; used in Lemma 1 and Lemma 2 to reason that a correct process cannot be used to double-vote.
domain assumption The identifier function id is collision-resistant: id(v) = id(w) implies v = w.
Stated at the start of Section 4; needed in Theorem 3 to conclude w = v from id(w) = id(v).
domain assumption The system satisfies n > 5f.
Stated in Section 2; used in Lemma 2 to ensure n - 3f > 2f, the key counting step.
domain assumption The application-specific validate() predicate defines external validity.
Stated in Section 2 and used in the freshness rule; the protocol does not define validate().

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Cite this review

Pith. "Pith review of Fast Tendermint: Speeding Up a Foundational Consensus Protocol." pith.science (2026). https://pith.science/paper/U6XBQ6N7

@misc{pith2026260813434,
  author       = {Pith},
  title        = {Pith review of: Fast Tendermint: Speeding Up a Foundational Consensus Protocol},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U6XBQ6N7}},
  note         = {Machine review of arXiv:2608.13434}
}

abstract

Tendermint is among the most widely studied and deployed Byzantine fault-tolerant (BFT) consensus protocols, owing in part to its native leader-rotation mechanism that subsumes complex view changes. Like most partially-synchronous BFT protocols, Tendermint tolerates $f < n/3$ Byzantine processes and decides in three communication steps. Motivated by the push for lower-latency blockchains, a recent line of work shows that consensus can be solved in two communication steps when $f < n/5$. We present Fast Tendermint, an adaptation of Tendermint to the $n > 5f$ setting that decides in two communication steps in the good case, while preserving Tendermint's leader-rotation structure. Fast Tendermint collapses Tendermint's prevote and precommit steps into a single voting step and merges the $locked$ and $valid$ state. We give proofs of agreement, validity, and termination, and a formal specification in Quint, a modern surface syntax for TLA+, used to model-check the protocol.

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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19 Leslie Lamport, Robert Shostak, and Marshall Pease. The Byzantine generals problem.ACM Transactions on Programming Languages and Systems, 4(3):382–401, 1982.doi:10.1145/ 357172.357176. 20 Gordon Y. Liao, Rachel Mayer, Adrian Soghoian, Sanket Jain, and Erik Tierney. Arc: An open layer-1 blockchain purpose-built for stablecoin finance.https://www.arc.io/...

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6 Christian Cachin, Klaus Kursawe, Frank Petzold, and Victor Shoup

arXiv:1807.04938. 6 Christian Cachin, Klaus Kursawe, Frank Petzold, and Victor Shoup. Secure and efficient asynchronous broadcast protocols. InAdvances in Cryptology — CRYPTO 2001, pages 524–541, 2001.doi:10.1007/3-540-44647-8_31. 7 Daniel Cason, Enrique Fynn, Nenad Milosevic, Zarko Milosevic, Ethan Buchman, and Fernando Pedone. The design, architecture a...

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