Crisis: Probabilistically Self Organizing Total Order in Unstructured P2P Networks

Mirco Richter

arxiv: 1907.07248 · v1 · pith:4BALGAAOnew · submitted 2019-07-13 · 💻 cs.DC

Crisis: Probabilistically Self Organizing Total Order in Unstructured P2P Networks

Mirco Richter This is my paper

Pith reviewed 2026-05-24 21:35 UTC · model grok-4.3

classification 💻 cs.DC

keywords total orderP2P networksprobabilistic convergenceasynchronous algorithmsself-organizing systemsCAP theorem

0 comments

The pith

A framework enables total order to converge probabilistically in unstructured peer-to-peer networks through fully local asynchronous decisions without signatures.

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

The paper develops a family of algorithms that produce a total ordering of events across nodes in decentralized networks lacking any fixed structure. These algorithms operate asynchronously and without signatures while adjusting their consistency and availability trade-offs according to detected attack severity. Local voting combined with probabilistic mechanisms drives convergence and keeps communication costs near optimal even in high-entropy settings. The overall approach is presented as a parameterized framework whose long-term behavior depends on the choice of several external tuning functions.

Core claim

The Crisis framework develops asynchronous, signature-free, fully local algorithms that probabilistically converge to a total order in high-entropy unstructured P2P networks while achieving near optimal communication efficiency and adapting consistency and availability based on attack severity.

What carries the argument

The Crisis framework, a parameterized family of algorithms using external functions for voting-weight, incentivation and punishment, difficulty oracle, and quorum-selector to tune the self-organization dynamics.

If this is right

Total order becomes possible in networks without central authority or cryptographic signatures.
The system can survive high entropy and attacks by choosing different consistency-availability compromises.
Communication remains near optimal regardless of network size or structure.
Behavior can be adjusted by selecting different external functions for incentives and quorums.

Where Pith is reading between the lines

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

Such a system might support decentralized applications requiring ordered events like ledgers or task scheduling.
Parameter choices could be optimized for specific network conditions to improve convergence speed.
Integration with existing unstructured overlays could test the framework's robustness in practice.

Load-bearing premise

The external functions for voting weight, incentives, difficulty, and quorum selection must be chosen to produce stable long-term dynamics.

What would settle it

A simulation or deployment in an unstructured P2P network under sustained attack where the order fails to converge or communication costs exceed optimal bounds.

read the original abstract

A framework for asynchronous, signature free, fully local and probabilistically converging total order algorithms is developed, that may survive in high entropy, unstructured Peer-to-Peer networks with near optimal communication efficiency. Regarding the natural boundaries of the CAP-theorem, Crisis chooses different compromises for consistency and availability, depending on the severity of the attack. The family is parameterized by a few constants and external functions called voting-weight, incentivation \& punishement, difficulty oracle and quorum-selector. These functions are necessary to fine tune the dynamics and very different long term behavior might appear, depending on any actual choice.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper sketches a parameterized framework for probabilistic total order in unstructured P2P networks but supplies no concrete functions, proofs, or results to show convergence actually occurs.

read the letter

The abstract introduces a family of algorithms for total order that are asynchronous, signature-free, fully local, and meant to work in high-entropy unstructured P2P settings with adaptive CAP tradeoffs. It positions the work as a framework rather than a single algorithm, with the behavior controlled by a handful of external functions: voting-weight, incentivation & punishment, difficulty oracle, and quorum-selector, plus a few constants. This parameterization is presented as a feature that lets the system tune itself to different conditions. That is the main new element on offer—an explicit admission that the dynamics depend on these choices and that different selections can produce very different long-term outcomes. The text does not claim to have solved the problem outright but rather to have defined a space in which solutions might live. That framing is at least honest about the dependencies. The obvious soft spot is that no specific functions are supplied, no convergence argument is given, and there are no simulations or examples. The abstract itself flags that the long-term behavior hinges on the concrete choices, yet nothing is shown to demonstrate that any choice delivers the advertised probabilistic convergence or resilience. Without at least one verified instantiation, the central claim stays at the level of an existence statement. The work is therefore too preliminary for a reading group or citation. It does not contain enough grounded material to justify sending it to referees.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a framework called Crisis for probabilistically self-organizing total order in unstructured P2P networks. The approach is claimed to be asynchronous, signature-free, fully local, and probabilistically convergent with near-optimal communication efficiency while adapting consistency/availability trade-offs to attack severity in accordance with the CAP theorem. The family of algorithms is parameterized by a small set of constants together with four external functions (voting-weight, incentivization & punishment, difficulty oracle, and quorum-selector) whose concrete choices determine long-term behavior.

Significance. If the framework can be instantiated with explicit functions that provably deliver the stated convergence, locality, and attack resilience properties, it would constitute a notable contribution to decentralized consensus by offering a flexible, signature-free mechanism suited to high-entropy unstructured networks.

major comments (2)

[Abstract] Abstract: the central claim that a family of algorithms 'may survive in high entropy, unstructured Peer-to-Peer networks with near optimal communication efficiency' and 'probabilistically converging' rests on the existence of suitable external functions, yet the manuscript supplies neither explicit definitions of these functions nor any convergence analysis, bounds, or simulation results demonstrating that any choice achieves the claimed properties.
[Abstract] Abstract: the statement that 'very different long term behavior might appear, depending on any actual choice' of the external functions is presented without accompanying criteria or invariants that the functions must satisfy, rendering the framework an existence claim whose supporting evidence is absent from the text.

minor comments (2)

[Abstract] Abstract: 'punishement' is a typographical error and should read 'punishment'.
[Abstract] Abstract: 'incentivation' is nonstandard; the conventional term is 'incentivization'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments. We address each major comment below and will revise the paper accordingly to strengthen the presentation of the framework.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that a family of algorithms 'may survive in high entropy, unstructured Peer-to-Peer networks with near optimal communication efficiency' and 'probabilistically converging' rests on the existence of suitable external functions, yet the manuscript supplies neither explicit definitions of these functions nor any convergence analysis, bounds, or simulation results demonstrating that any choice achieves the claimed properties.

Authors: The manuscript introduces Crisis as a parameterized framework whose concrete behavior is determined by the choice of the four external functions. The current version focuses on defining the overall structure, the role of each parameter, and the high-level adaptation to attack severity under the CAP theorem. We acknowledge that the abstract claims would be better supported by at least one fully worked example. In the revision we will add an explicit section that supplies concrete definitions for all four functions, a sketch of a probabilistic convergence argument under standard assumptions on the network entropy, and simulation results for the resulting instantiation. revision: yes
Referee: [Abstract] Abstract: the statement that 'very different long term behavior might appear, depending on any actual choice' of the external functions is presented without accompanying criteria or invariants that the functions must satisfy, rendering the framework an existence claim whose supporting evidence is absent from the text.

Authors: We agree that the manuscript would benefit from stating the minimal invariants or interface contracts that any admissible choice of the external functions must obey in order to preserve the claimed locality, asynchrony, and signature-free properties. The revision will include a short subsection that lists these necessary conditions (e.g., monotonicity of the voting-weight function, correctness of the difficulty oracle under bounded network entropy) together with a brief argument why they suffice for the framework-level guarantees. revision: yes

Circularity Check

1 steps flagged

Convergence properties depend on choice of unspecified external tuning functions

specific steps

fitted input called prediction [Abstract]
"The family is parameterized by a few constants and external functions called voting-weight, incentivation & punishement, difficulty oracle and quorum-selector. These functions are necessary to fine tune the dynamics and very different long term behavior might appear, depending on any actual choice."

The framework is asserted to deliver asynchronous, signature-free, fully local and probabilistically converging total order. Yet the text defines the family such that its dynamics and behavior (including convergence) are controlled by the choice of these external functions. The claimed convergence therefore reduces to the existence of appropriately tuned inputs rather than being derived from the core algorithm independent of those inputs.

full rationale

The paper's central claim is the development of a framework for probabilistically converging total order. However, the abstract states that this family is parameterized by external functions whose concrete choice determines long-term behavior and that these functions are necessary to fine-tune the dynamics. This makes the claimed convergence a consequence of selecting suitable external functions rather than an independent derivation from the framework equations or structure. No specific functions, proofs, or instantiations are supplied in the provided text to break the dependence. This matches the fitted_input_called_prediction pattern with partial circularity (score 6) but is not fully self-definitional or load-bearing via self-citation.

Axiom & Free-Parameter Ledger

5 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence and suitable choice of external tuning functions and constants, plus domain assumptions about the network environment; no independent evidence or derivations for these are provided in the abstract.

free parameters (5)

voting-weight function
External function to assign weights to votes, required to tune dynamics.
incentivation & punishment function
External function for incentives and punishments to shape behavior.
difficulty oracle
External function for setting difficulty levels.
quorum-selector
External function to select quorums.
a few constants
Constants parameterizing the algorithm family.

axioms (2)

domain assumption The target networks are high entropy and unstructured P2P.
Invoked to claim survival and near-optimal efficiency in such settings.
ad hoc to paper Suitable choices of the external functions exist that produce the claimed convergence and attack adaptation.
Central to the framework's claimed functionality.

pith-pipeline@v0.9.0 · 5618 in / 1553 out tokens · 29030 ms · 2026-05-24T21:35:38.046737+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The family is parameterized by a few constants and external functions called voting-weight, incentivation & punishement, difficulty oracle and quorum-selector.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Crisis extends the timelike causality between messages into a probabilistically converging total order

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages

[1]

A.; Bessani, A.N.; Fraga, J.S.; Greve, F

Alchieri, E. A.; Bessani, A.N.; Fraga, J.S.; Greve, F. : (2008) Byzantine Consensus with Unknown Participants. In Proceedings of the 12th International Conference on Principles of Distributed Systems (OPODIS ’08). Springer- Verlag, Berlin, Heidelberg, 22-40

work page 2008
[2]

: (2016) The Swirlds hashgraph con- sensus algorithm: Fair, fast, Byzantine fault tolerance, Swrirlds tech report, SWIRLDS-TR- 2016-01

Baird, L. : (2016) The Swirlds hashgraph con- sensus algorithm: Fair, fast, Byzantine fault tolerance, Swrirlds tech report, SWIRLDS-TR- 2016-01

work page 2016
[3]

Beck A.: (2002) Hashcash - A Denial of Service Counter-Measure

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Chen, J.; Micali, S. : (2016). Algorand

work page 2016
[5]

: (2018) Protocol for Asynchronous, Reliable, Secure and Eﬃcient Consensus (PARSEC)

Chevalier, P.; Kaminski, B.; Hutchison, F.; Ma, Q.; Sharma, S. : (2018) Protocol for Asynchronous, Reliable, Secure and Eﬃcient Consensus (PARSEC)

work page 2018
[6]

: (2018) Block- mania: from Block DAGs to Consensus

Danezis, G.; Hrycyszyn, D. : (2018) Block- mania: from Block DAGs to Consensus

work page 2018
[7]

: (1997) An Optimal Probabilistic Algorithm for Synchronous Byzan- tine Agreement

Feldman P., Micali S. : (1997) An Optimal Probabilistic Algorithm for Synchronous Byzan- tine Agreement. (Preliminary version in STOC 88.) SIAM J. on Computing

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[8]

Lamport, L.: (1978) Time, clocks, and the or- dering of events in a distributed system, Com- mun. Assoc. Comput. Mach. 21, 558-565

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[9]

: (2018)

Micali, S. : (2018). Byzantine Agreement , Made Trivial

work page 2018
[10]

Moser and P

Louise E. Moser and P. M. Melliar- Smith: (1999) Byzantine-Resistant Total Or- dering Algorithms. Inf. Comput.. 150. 75-111

work page 1999
[11]

: (2009) Bitcoin: A Peer-to- Peer Electronic Cash System

Nakamoto, S. : (2009) Bitcoin: A Peer-to- Peer Electronic Cash System

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[12]

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work page 2014

[1] [1]

A.; Bessani, A.N.; Fraga, J.S.; Greve, F

Alchieri, E. A.; Bessani, A.N.; Fraga, J.S.; Greve, F. : (2008) Byzantine Consensus with Unknown Participants. In Proceedings of the 12th International Conference on Principles of Distributed Systems (OPODIS ’08). Springer- Verlag, Berlin, Heidelberg, 22-40

work page 2008

[2] [2]

: (2016) The Swirlds hashgraph con- sensus algorithm: Fair, fast, Byzantine fault tolerance, Swrirlds tech report, SWIRLDS-TR- 2016-01

Baird, L. : (2016) The Swirlds hashgraph con- sensus algorithm: Fair, fast, Byzantine fault tolerance, Swrirlds tech report, SWIRLDS-TR- 2016-01

work page 2016

[3] [3]

Beck A.: (2002) Hashcash - A Denial of Service Counter-Measure

work page 2002

[4] [4]

: (2016)

Chen, J.; Micali, S. : (2016). Algorand

work page 2016

[5] [5]

: (2018) Protocol for Asynchronous, Reliable, Secure and Eﬃcient Consensus (PARSEC)

Chevalier, P.; Kaminski, B.; Hutchison, F.; Ma, Q.; Sharma, S. : (2018) Protocol for Asynchronous, Reliable, Secure and Eﬃcient Consensus (PARSEC)

work page 2018

[6] [6]

: (2018) Block- mania: from Block DAGs to Consensus

Danezis, G.; Hrycyszyn, D. : (2018) Block- mania: from Block DAGs to Consensus

work page 2018

[7] [7]

: (1997) An Optimal Probabilistic Algorithm for Synchronous Byzan- tine Agreement

Feldman P., Micali S. : (1997) An Optimal Probabilistic Algorithm for Synchronous Byzan- tine Agreement. (Preliminary version in STOC 88.) SIAM J. on Computing

work page 1997

[8] [8]

Lamport, L.: (1978) Time, clocks, and the or- dering of events in a distributed system, Com- mun. Assoc. Comput. Mach. 21, 558-565

work page 1978

[9] [9]

: (2018)

Micali, S. : (2018). Byzantine Agreement , Made Trivial

work page 2018

[10] [10]

Moser and P

Louise E. Moser and P. M. Melliar- Smith: (1999) Byzantine-Resistant Total Or- dering Algorithms. Inf. Comput.. 150. 75-111

work page 1999

[11] [11]

: (2009) Bitcoin: A Peer-to- Peer Electronic Cash System

Nakamoto, S. : (2009) Bitcoin: A Peer-to- Peer Electronic Cash System

work page 2009

[12] [12]

Spivak, D. I. : (2014) Category Theory for the Sciences. MIT Press. 31

work page 2014