Pith. sign in

REVIEW 2 major objections 5 minor 41 references

Consensus is collapse under evidence: protocols differ by how they make communication history safe to project into a value or prefix.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-14 13:53 UTC pith:QL35A4LC

load-bearing objection A careful denotational vocabulary for reading consensus as collapse of communication evidence; useful comparison frame, not a theorem. the 2 major comments →

arxiv 2607.10152 v1 pith:QL35A4LC submitted 2026-07-11 cs.DC

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

Tomislav Grospi\'c This is my paper
classification cs.DC
keywords consensuscollapse policycommunication evidenceevidence horizonorder-2 carrierFLPatomic broadcastDAG consensus
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that consensus protocols are usually described by their final artifact—a decided value, log, or finalized prefix—and that this output-first view hides the communication evidence that makes those artifacts safe. It models distributed execution as an order-2 evidence state induced by messages, votes, certificates, and causal structure, and treats classical outputs as order-1 projections of that state. Under that reading, protocols become comparable as collapse policies: each specifies which evidence counts as legitimate, which finite horizon it inspects, when it projects to a value or prefix, and how it repairs or defers when the visible evidence is insufficient. The classical impossibility lineage is reread the same way: FLP constrains guaranteed terminal collapse under full asynchrony and one crash, not the ability of communication to accumulate structure. The contribution is a denotational specification framework for comparing real protocols by the evidence they retain and the collapse they permit, not a new impossibility theorem or a replacement for protocol-specific proofs.

Core claim

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. The paper’s claim is that consensus is collapse under evidence: safety lives in the communication carrier and the conditions under which distinctions may stop mattering, not in the decided value alone.

What carries the argument

Collapse-policy specification in normal form Ht —L→ Et —R→ Et|R —C→ P: a communication carrier, legitimacy extraction, evidence horizon, and partial collapse rule that emits a value or prefix only when the visible evidence determines an invariant observation (or refuses and repairs/defers). Collapse debt names the gap when the chosen horizon still admits refinements that could change the output.

Load-bearing premise

That this shared normal form of carriers, legitimacy, horizons, and collapse rules is a faithful semantic lens for comparing crash, Byzantine, randomized, stake-weighted, sampling, and DAG protocols without distorting their actual safety arguments.

What would settle it

Exhibit a representative consensus or atomic-broadcast protocol whose safety argument cannot be stated as legitimacy-plus-horizon-plus-collapse-or-repair without adding essential structure the framework discards, or show that two protocols the paper treats as the same collapse policy have incompatible safety conditions under that encoding.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Protocol comparison can be stated in shared terms—legitimacy, horizon width, compression, collapse, and repair—rather than only by terminal artifacts or phase names.
  • FLP, set agreement, and topological results read as constraints on guaranteed terminal collapse and output-carrier width, not as denials that communication history can grow.
  • Fallback, view-change, undecided-slot, and random-leader mechanisms become explicit management of collapse debt rather than incidental engineering.
  • Design can begin by choosing the evidence carrier and when collapse is allowed, including adaptive horizons and carrier-preserving finality with prefixes as projections.
  • Leader-mediated certificate compression and full-gossip DAG visibility sit on a spectrum of how much order-2 evidence is disseminated before collapse.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the framework holds, performance and safety debates that only count rounds or message complexity may mis-rank protocols that differ mainly in when they discard evidence.
  • The same lens could be applied to reconfiguration, light-client verification, and cross-chain bridges, which also collapse remote evidence into a local trusted prefix.
  • A machine-checkable encoding of the normal form would let implementers state and compare collapse policies independently of protocol-specific proofs.
  • Protocols that expose undecided or skip outcomes (as in the Mysticeti case) may be the clearest operational tests of whether collapse debt is a useful design primitive.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper proposes a denotational comparison framework for fault-tolerant consensus and atomic-broadcast protocols. It treats distributed execution as an order-2 communication-induced evidence carrier and classical consensus outputs (values, logs, finalized prefixes) as order-1 projections of that carrier. Protocols are specified in a shared normal form H → L → E → R → V → C → P (evidence domain, legitimacy extraction, horizon, collapse, and repair/deferral), with classical impossibility results reread as constraints on guaranteed terminal collapse rather than on evidence accumulation. Main case studies (Lamport ordering, Byzantine Generals, Paxos, HotStuff, CBC Casper, Cordial Miners, Mysticeti-C) and a broad appendix catalog instantiate the form; the author explicitly disclaims new impossibility theorems and replacement of protocol-specific proofs.

Significance. If accepted as a semantic specification layer rather than a theorem paper, the contribution is useful: it cleanly separates legitimacy (quorums, certificates, slices, sampling, estimators, DAG support) from collapse policy (horizon, projection, repair), and it gives a shared vocabulary for comparing crash, Byzantine, randomized, PoS, sampling, and DAG protocols. The collapse-debt reading of Mysticeti-C’s direct/indirect rules and the Cordial Miners comparison are concrete comparative payoffs, as is the communication-surface analysis distinguishing full-gossip DAG visibility from leader/QC compression. The manuscript is careful about non-claims (FLP is not refuted; model-identical reductions are not asserted). Strengths are interpretive clarity and breadth of coverage rather than machine-checked proofs or new lower bounds.

major comments (2)
  1. [§3, Def. 3.2; §2.3, Def. 2.6] Def. 3.2 (Realization law) and Def. 2.6 (Semantic collapse) are stated as denotational obligations, but the manuscript never discharges them for any protocol with an explicit denotation map [[·]] and a non-vacuous Adm/obs pair. The case studies remain schematic normal-form readings. For a claim of denotational specification (not only informal taxonomy), at least one fully worked instance—e.g., single-slot Paxos or the Mysticeti-C slot derivation in §7.9—should exhibit carriers, L/R/C, Adm, obs, and a check that emitted outputs preserve the specified meaning. Without that, the central “specification framework” claim stays aspirational.
  2. [§8 Synthesis] The comparative force of the normal form needs a sharper criterion for sameness vs. difference of collapse policies. §8.2–8.3 give useful axes (legitimacy locus, horizon width, refusal of collapse, discarded distinctions), but it remains unclear when two protocols are judged equivalent under the framework versus merely rewritable into the same template by construction. A short subsection stating what would count as a non-trivial equivalence or distinction (e.g., same L and C but different R, or same carrier with different repair) would make the contribution falsifiable as a comparison method rather than only a rewriting scheme.
minor comments (5)
  1. [§1 Introduction; Order terminology] The terms “order-2” and “order-1” conflict with standard distributed-computing usage (partial/total orders, topological order). A brief note early in §1 or §2 that these are semantic labels for carrier vs. projection, not algebraic order theory, would reduce confusion.
  2. [§3.1 Protocol vocabulary dictionary] Table in §3.1 maps protocol terms to semantic roles but is not numbered or captioned; give it a formal table number and caption for citation.
  3. [Appendix A] Appendix entries are explicitly schematic; a one-sentence header reminder that they are coverage checks, not proofs, would help readers who land on the appendix first.
  4. [§4 FLP as Order-Collapse Constraint] In §4, the translation of bivalence to fibers of C is clear; a single sentence linking univalence to Def. 2.6’s invariance under ↑Adm would tighten the bridge between FLP and the semantic-collapse definition.
  5. [References] References are thorough; consider adding a pointer to recent formalizations of HotStuff/Jolteon or CBC Casper if space allows, since the paper leans on those mechanisms as witnesses of invariance.

Circularity Check

0 steps flagged

No significant circularity: denotational framework is definitional by design, with no fitted predictions, self-citation chains, or uniqueness imports that force the central claim.

full rationale

The paper's contribution is explicitly scoped as a denotational vocabulary and normal form (Ht L o Et R o Et|R C o P; Defs. 2.1–3.2) for re-reading existing protocols and the FLP–set-agreement–topology lineage as collapse policies. It repeatedly disclaims new theorems, model subsumption, or replacement of protocol proofs (Abstract; §1 Non-contributions; §6; §9). Instantiations (Lamport, BGP, Paxos, HotStuff, CBC Casper, Cordial Miners, Mysticeti-C, appendix) are interpretive mappings that fit the form by construction once the carriers and maps are named; this is expected for a specification framework and does not reduce any external prediction or uniqueness claim to its own inputs. There are no free parameters fitted to data and then re-presented as predictions, no load-bearing self-citations of prior uniqueness theorems by the same author, and no ansatz smuggled via citation. Realization law (Def. 3.2) and semantic-collapse invariance (Def. 2.6) are stated as obligations, not derived results that loop. Mild definitional packaging of the thesis (“consensus is collapse under evidence”) is present but does not constitute circular derivation of a first-principles claim. Score remains at the low end of the 0–2 band for honest non-finding on a self-contained interpretive paper.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 3 invented entities

This is a conceptual/denotational paper. It rests on standard distributed-computing background (FLP, set agreement, topology, classical protocol mechanisms) plus paper-specific semantic packaging. There are no fitted numeric parameters. The load-bearing additions are the order terminology, collapse-policy normal form, and collapse-debt reading used to unify protocol comparison.

axioms (5)
  • domain assumption FLP impossibility for deterministic consensus under full asynchrony with one crash failure remains valid as stated.
    Invoked in §4 and the abstract; the paper reinterprets but does not re-prove or weaken the theorem.
  • domain assumption Classical protocol safety mechanisms (quorum intersection, certificates, locks, estimators, DAG support, sampling confidence, etc.) correctly supply decision-grade evidence in their published models.
    Used throughout §§7–8 and appendix instantiations; the framework assumes those legitimacy witnesses work as claimed by the source papers.
  • ad hoc to paper Distributed execution can be treated as an order-2 communication/evidence carrier whose terminal consensus outputs are order-1 projections.
    Core semantic move of §§1–3; not a standard theorem, but the paper’s organizing premise.
  • ad hoc to paper A protocol’s essential comparative structure is captured by legitimacy extraction L, horizon R, collapse C, and repair/deferral when C is undefined.
    Definition 3.1 and the normal form H→L→R→C; this is the paper’s denotational claim about what matters for comparison.
  • domain assumption Topological and set-agreement results constrain structure-preserving maps from history/view carriers to output carriers.
    §5 cites Chaudhuri, Borowsky–Gafni, Herlihy–Shavit, Saks–Zaharoglou as the impossibility ladder supporting the carrier/output reading.
invented entities (3)
  • Collapse-policy specification (carriers H,E,V,P and maps L,R,C) no independent evidence
    purpose: Provide a shared denotational normal form for comparing consensus protocols.
    Introduced in §3 as the paper’s main formal packaging; not independently measured outside this framework.
  • Collapse debt no independent evidence
    purpose: Name the gap between inspected evidence and evidence needed for invariant terminal observation, and interpret repair/fallback rules.
    Defined in §2.3 and used especially for Mysticeti and DAG protocols; a metaphor/analytic construct rather than an external measurable quantity.
  • Order-2 evidence state / order-1 terminal artifact distinction no independent evidence
    purpose: Separate communication history from projected values/logs/prefixes.
    Semantic terminology introduced early and used throughout; useful packaging of known history-vs-output ideas.

pith-pipeline@v1.1.0-grok45 · 35668 in / 3331 out tokens · 27551 ms · 2026-07-14T13:53:20.040852+00:00 · methodology

0 comments
read the original 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. This paper makes that carrier explicit: distributed execution is read as an order-2 evidence state induced by communication, while classical consensus outputs are 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 communication evidence into a value or prefix, and how it repairs or defers collapse when the visible evidence is insufficient. The impossibility lineage supports the same distinction. FLP is not a statement that communication cannot accumulate structure; it constrains deterministic guaranteed collapse to a terminal decision under full asynchrony with one crash failure. Set agreement then exposes the width of the output carrier, and topological distributed computing asks when a history/view carrier admits a structure-preserving map to an output carrier. The contribution is not a new impossibility theorem or a replacement for protocol-specific proofs, but a denotational specification framework: consensus is collapse under evidence.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

41 extracted references · 11 canonical work pages · 4 internal anchors

  1. [1]

    Time, Clocks, and the Ordering of Events in a Distributed System.Communi- cations of the ACM21(7):558–565, 1978

    Leslie Lamport. Time, Clocks, and the Ordering of Events in a Distributed System.Communi- cations of the ACM21(7):558–565, 1978. DOI:https://doi.org/10.1145/359545.359563. URL:https://lamport.azurewebsites.net/pubs/time-clocks.pdf

    doi:10.1145/359545.359563 1978

  2. [2]

    The Part-Time Parliament.ACM Transactions on Computer Systems 16(2):133–169, 1998

    Leslie Lamport. The Part-Time Parliament.ACM Transactions on Computer Systems 16(2):133–169, 1998. DOI:https://doi.org/10.1145/279227.279229

    doi:10.1145/279227.279229 1998

  3. [3]

    Paxos Made Simple.ACM SIGACT News32(4):51–58, 2001

    Leslie Lamport. Paxos Made Simple.ACM SIGACT News32(4):51–58, 2001. URL:https: //lamport.azurewebsites.net/pubs/paxos-simple.pdf

    2001

  4. [4]

    In Search of an Understandable Consensus Algorithm

    Diego Ongaro and John Ousterhout. In Search of an Understandable Consensus Algorithm. InProceedings of the 2014 USENIX Annual Technical Conference, 2014. URL:https://www. usenix.org/conference/atc14/technical-sessions/presentation/ongaro

    2014

  5. [5]

    Fischer, Nancy A

    Michael J. Fischer, Nancy A. Lynch, and Michael S. Paterson. Impossibility of distributed consensus with one faulty process.Journal of the ACM32(2):374–382, 1985. DOI:https: //doi.org/10.1145/3149.214121. URL:https://groups.csail.mit.edu/tds/papers/ Lynch/jacm85.pdf

    doi:10.1145/3149.214121 1985

  6. [6]

    Agreement is harder than consensus: Set consensus problems in totally asynchronous systems

    Soma Chaudhuri. Agreement is harder than consensus: Set consensus problems in totally asynchronous systems. InProceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing, pages 311–324, 1990. DOI:https://doi.org/10.1145/93385.93428

    work page doi:10.1145/93385.93428 1990

  7. [7]

    Generalized FLP impossibility result for t-resilient asyn- chronous computations

    Elizabeth Borowsky and Eli Gafni. Generalized FLP impossibility result for t-resilient asyn- chronous computations. InProceedings of the 25th Annual ACM Symposium on Theory of Computing, pages 91–100, 1993. DOI:https://doi.org/10.1145/167088.167119

    work page doi:10.1145/167088.167119 1993

  8. [8]

    The topological structure of asynchronous computabil- ity.Journal of the ACM46(6):858–923, 1999

    Maurice Herlihy and Nir Shavit. The topological structure of asynchronous computabil- ity.Journal of the ACM46(6):858–923, 1999. DOI:https://doi.org/10.1145/331524. 331529. URL:https://www.cs.yale.edu/homes/aspnes/pinewiki/attachments/CS425% 282f%29Schedule/HerlihyShavit1999.pdf

    doi:10.1145/331524 1999

  9. [9]

    Wait-free k-set agreement is impossible: The topol- ogy of public knowledge

    Michael Saks and Fotios Zaharoglou. Wait-free k-set agreement is impossible: The topol- ogy of public knowledge. InProceedings of the 25th Annual ACM Symposium on Theory of Computing, pages 101–110, 1993. DOI:https://doi.org/10.1145/167088.167122. 45

    work page doi:10.1145/167088.167122 1993

  10. [10]

    The Byzantine Generals Problem.ACM Transactions on Programming Languages and Systems4(3):382–401, 1982

    Leslie Lamport, Robert Shostak, and Marshall Pease. The Byzantine Generals Problem.ACM Transactions on Programming Languages and Systems4(3):382–401, 1982. DOI:https:// doi.org/10.1145/357172.357176

    doi:10.1145/357172.357176 1982

  11. [11]

    Consensus in the presence of par- tial synchrony.Journal of the ACM35(2):288–323, 1988

    Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Consensus in the presence of par- tial synchrony.Journal of the ACM35(2):288–323, 1988. DOI:https://doi.org/10.1145/ 42282.42283. URL:https://groups.csail.mit.edu/tds/papers/Lynch/jacm88.pdf

    arXiv 1988

  12. [12]

    Unreliable failure detectors for reliable distributed systems.Journal of the ACM43(2):225–267, 1996

    Tushar Deepak Chandra and Sam Toueg. Unreliable failure detectors for reliable distributed systems.Journal of the ACM43(2):225–267, 1996. DOI:https://doi.org/10.1145/226643. 226647

    work page doi:10.1145/226643 1996

  13. [13]

    Another Advantage of Free Choice: Completely Asynchronous Agreement Protocols

    Michael Ben-Or. Another Advantage of Free Choice: Completely Asynchronous Agreement Protocols. InProceedings of the 2nd Annual ACM Symposium on Principles of Distributed Computing, pages 27–30, 1983. DOI:https://doi.org/10.1145/800221.806707

    work page doi:10.1145/800221.806707 1983

  14. [14]

    Michael O. Rabin. Randomized Byzantine Generals. InProceedings of the 24th Annual Sym- posium on Foundations of Computer Science, pages 403–409, 1983. DOI:https://doi.org/ 10.1109/SFCS.1983.48

    work page doi:10.1109/sfcs.1983.48 1983

  15. [15]

    FastAsynchronousByzantineAgreement with OptimalResilience

    Ran Canettiand TalRabin. FastAsynchronousByzantineAgreement with OptimalResilience. InProceedings of the 25th Annual ACM Symposium on Theory of Computing, pages 42–51,

  16. [16]

    DOI:https://doi.org/10.1145/167088.167105

    work page doi:10.1145/167088.167105

  17. [17]

    The Honey Badger of BFT Protocols

    Andrew Miller, Yu Xia, Kyle Croman, Elaine Shi, and Dawn Song. The Honey Badger of BFT Protocols. InProceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, pages 31–42, 2016. DOI:https://doi.org/10.1145/2976749. 2978399. URL:https://eprint.iacr.org/2016/199

    doi:10.1145/2976749 2016

  18. [18]

    Practical Byzantine Fault Tolerance

    Miguel Castro and Barbara Liskov. Practical Byzantine Fault Tolerance. In Proceedings of the 3rd Symposium on Operating Systems Design and Implemen- tation, 1999. URL:https://www.usenix.org/conference/osdi-99/presentation/ practical-byzantine-fault-tolerance

    1999

  19. [19]

    The Stellar Consensus Protocol: A Federated Model for Internet-level Consensus

    David Mazieres. The Stellar Consensus Protocol: A Federated Model for Internet-level Consensus. Stellar Development Foundation, 2015. URL:https://stellar.org/papers/ stellar-consensus-protocol.pdf

    2015

  20. [20]

    Reiter, Guy Golan Gueta, and Ittai Abraham

    Maofan Yin, Dahlia Malkhi, Michael K. Reiter, Guy Golan Gueta, and Ittai Abraham. Hot- Stuff: BFT Consensus in the Lens of Blockchain. InProceedings of the 2019 ACM Sym- posium on Principles of Distributed Computing, 2019. arXiv:1803.05069. URL:https: //arxiv.org/abs/1803.05069. DOI:https://doi.org/10.1145/3293611.3331591

    Pith/arXiv arXiv doi:10.1145/3293611.3331591 2019

  21. [21]

    Tendermint: Consensus without Mining

    Jae Kwon. Tendermint: Consensus without Mining. Technical report, 2014. URL:https: //tendermint.com/static/docs/tendermint.pdf

    2014

  22. [22]

    Chan and Elaine Shi

    Benjamin Y. Chan and Elaine Shi. Streamlet: Textbook Streamlined Blockchains. InPro- ceedings of the 2nd ACM Conference on Advances in Financial Technologies, 2020. DOI: https://doi.org/10.1145/3419614.3423256. URL:https://eprint.iacr.org/2020/088

    doi:10.1145/3419614.3423256 2020

  23. [23]

    Algorand: Scaling Byzantine Agreements for Cryptocurrencies

    Yossi Gilad, Rotem Hemo, Silvio Micali, Georgios Vlachos, and Nickolai Zeldovich. Algorand: Scaling Byzantine Agreements for Cryptocurrencies. InProceedings of the 26th Symposium on 46 Operating Systems Principles, pages 51–68, 2017. DOI:https://doi.org/10.1145/3132747. 3132757. URL:https://eprint.iacr.org/2017/454

    doi:10.1145/3132747 2017

  24. [24]

    Jolteon and Ditto: Network-Adaptive Efficient Consensus with Asynchronous Fallback

    Rati Gelashvili, Lefteris Kokoris-Kogias, Alberto Sonnino, Alexander Spiegelman, and Zhuolun Xiang. Jolteon and Ditto: Network-Adaptive Efficient Consensus with Asynchronous Fall- back. InFinancial Cryptography and Data Security, pages 296–315, 2022. DOI:https: //doi.org/10.1007/978-3-031-18283-9_14. arXiv:2106.10362v4. URL:https://arxiv. org/abs/2106.10362

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/978-3-031-18283-9_14 2022

  25. [25]

    HotStuff-2: Optimal Two-Phase Responsive BFT

    Dahlia Malkhi and Kartik Nayak. HotStuff-2: Optimal Two-Phase Responsive BFT. Cryptol- ogy ePrint Archive, Paper 2023/397, 2023. URL:https://eprint.iacr.org/2023/397

    2023

  26. [26]

    Ouroboros: A Provably Secure Proof-of-Stake Blockchain Protocol

    Aggelos Kiayias, Alexander Russell, Bernardo David, and Roman Oliynykov. Ouroboros: A Provably Secure Proof-of-Stake Blockchain Protocol. InAdvances in Cryptology – CRYPTO 2017, pages 357–388, 2017. DOI:https://doi.org/10.1007/978-3-319-63688-7_12. URL: https://eprint.iacr.org/2016/889

    doi:10.1007/978-3-319-63688-7_12 2017

  27. [27]

    Ouroboros Praos: An Adaptively-Secure, Semi-synchronous Proof-of-Stake Blockchain

    Bernardo David, Peter Gazi, Aggelos Kiayias, and Alexander Russell. Ouroboros Praos: An Adaptively-Secure, Semi-synchronous Proof-of-Stake Blockchain. InAdvances in Cryp- tology – EUROCRYPT 2018, pages 66–98, 2018. DOI:https://doi.org/10.1007/ 978-3-319-78375-8_3. URL:https://eprint.iacr.org/2017/573

    2018

  28. [28]

    GRANDPA: a Byzantine Finality Gadget

    Alistair Stewart and Eleftherios Kokoris-Kogias. GRANDPA: a Byzantine Finality Gadget. arXiv:2007.01560, 2020. DOI:https://doi.org/10.48550/arXiv.2007.01560. URL:https: //arxiv.org/abs/2007.01560

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2007.01560 2007

  29. [29]

    Casper the Friendly Finality Gadget

    Vitalik Buterin and Virgil Griffith. Casper the Friendly Finality Gadget. arXiv:1710.09437,

    Pith/arXiv arXiv

  30. [30]

    URL:https://arxiv.org/ abs/1710.09437

    DOI:https://doi.org/10.48550/arXiv.1710.09437. URL:https://arxiv.org/ abs/1710.09437

    Pith/arXiv arXiv doi:10.48550/arxiv.1710.09437

  31. [31]

    Scal- able and Probabilistic Leaderless BFT Consensus through Metastability

    Team Rocket, Maofan Yin, Kevin Sekniqi, Robbert van Renesse, and Emin Gun Sirer. Scal- able and Probabilistic Leaderless BFT Consensus through Metastability. arXiv:1906.08936,

    Pith/arXiv arXiv 1906

  32. [32]

    URL:https://arxiv.org/ abs/1906.08936

    DOI:https://doi.org/10.48550/arXiv.1906.08936. URL:https://arxiv.org/ abs/1906.08936

    Pith/arXiv arXiv doi:10.48550/arxiv.1906.08936 1906

  33. [33]

    Casper the Friendly Ghost: A Correct-by-Construction Blockchain Consensus Protocol

    Vlad Zamfir. Casper the Friendly Ghost: A Correct-by-Construction Blockchain Consensus Protocol. Draft v0.1, Ethereum Foundation, 2017. URL:https://raw.githubusercontent. com/vladzamfir/research/master/papers/CasperTFG/CasperTFG.pdf

    2017

  34. [34]

    All You Need is DAG

    Idit Keidar, Eleftherios Kokoris-Kogias, Oded Naor, and Alexander Spiegelman. All You Need is DAG. arXiv:2102.08325v2, 2021. URL:https://arxiv.org/abs/2102.08325

    Pith/arXiv arXiv 2021

  35. [35]

    The Swirlds Hashgraph Consensus Algorithm: Fair, Fast, Byzantine Fault Tol- erance

    Leemon Baird. The Swirlds Hashgraph Consensus Algorithm: Fair, Fast, Byzantine Fault Tol- erance. Swirlds Technical Report SWIRLDS-TR-2016-01, 2016. URL:https://www.swirlds. com/downloads/SWIRLDS-TR-2016-01.pdf

    2016

  36. [36]

    Aleph: Efficient Atomic Broadcast in Asynchronous Networks with Byzantine Nodes

    Adam Gagol, Damian Lesniak, Damian Straszak, and Michal Swietek. Aleph: Efficient Atomic Broadcast in Asynchronous Networks with Byzantine Nodes. InProceedings of the 1st ACM Conference on Advances in Financial Technologies, pages 214–228, 2019. DOI:https://doi. org/10.1145/3318041.3355467. URL:https://arxiv.org/abs/1908.05156. 47

    doi:10.1145/3318041.3355467 2019

  37. [37]

    Narwhal and Tusk: A DAG-based Mempool and Efficient BFT Consensus

    George Danezis, Lefteris Kokoris-Kogias, Alberto Sonnino, and Alexander Spiegelman. Nar- whal and Tusk: A DAG-based Mempool and Efficient BFT Consensus. InProceedings of EuroSys 2022, 2022. arXiv:2105.11827v4. URL:https://arxiv.org/abs/2105.11827. DOI: https://doi.org/10.1145/3492321.3519594

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1145/3492321.3519594 2022

  38. [38]

    Bull- shark: DAG BFT Protocols Made Practical

    Alexander Spiegelman, Neil Giridharan, Alberto Sonnino, and Lefteris Kokoris-Kogias. Bull- shark: DAG BFT Protocols Made Practical. arXiv:2201.05677v3, 2022. URL:https: //arxiv.org/abs/2201.05677

    Pith/arXiv arXiv 2022

  39. [39]

    Mysticeti: Reaching the Limits of Latency with Uncertified DAGs

    Kushal Babel, Andrey Chursin, George Danezis, Anastasios Kichidis, Lefteris Kokoris-Kogias, Arun Koshy, Alberto Sonnino, and Mingwei Tian. Mysticeti: Reaching the Limits of Latency with Uncertified DAGs. arXiv:2310.14821v6, 2025. URL:https://arxiv.org/abs/2310. 14821

    arXiv 2025

  40. [40]

    Cordial Miners: Fast and Efficient Consensus for Every Eventuality

    Idit Keidar, Oded Naor, Ouri Poupko, and Ehud Shapiro. Cordial Miners: Fast and Efficient Consensus for Every Eventuality. In37th International Symposium on Distributed Comput- ing, LIPIcs 281:26:1–26:22, 2023. arXiv:2205.09174v6. URL:https://arxiv.org/abs/2205. 09174. DOI:https://doi.org/10.4230/LIPIcs.DISC.2023.26

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.4230/lipics.disc.2023.26 2023

  41. [41]

    The Blocklace: A Byzantine-repelling and Universal Conflict-free Replicated Data Type

    Paulo Sérgio Almeida and Ehud Shapiro. The Blocklace: A Byzantine-repelling and Universal Conflict-free Replicated Data Type. arXiv:2402.08068, 2024. URL:https://arxiv.org/abs/ 2402.08068. 48

    Pith/arXiv arXiv 2024