The Swirlds Hashgraph Consensus Algorithm: Fair, Fast, Byzantine Fault Tolerance

01 Claim ledger

What the paper is allowed to say

Each row is a sentence already in the study. The status is the same on every row: a model claim, not a live measurement.

1. Claim 01 · Paper model

   Gossip about gossip

   A node tells a random peer everything it knows, including whom it has already told. The history of that gossip is a directed graph. The graph is the input to consensus.

2. Claim 02 · Paper model

   Virtual voting

   Because every node can compute the same graph, each node can calculate how the others would have voted. The paper's claim is that the ballots do not need to cross the network.

3. Claim 03 · Paper model

   Fairness is ordered by receipt

   The paper defines a timestamp from when an event reached a supermajority, and it orders transactions by that time. The fairness claim is this definition, not a general promise about markets.

4. Claim 04 · Paper model

   The set is permissioned in the core argument

   Virtual voting assumes you know who the members are. An open membership race is a different problem. Hedera's later council and permissionless work should not be back-dated into the proof.

5. Claim 05 · Paper model

   Asynchronous Byzantine fault tolerance is the target

   The paper argues safety without a leader and without a round timeout as the primary tool. The argument depends on the gossip graph eventually connecting. Partitions still delay the moment a supermajority sees an event.

02 Three cuts

Observation, model, falsifier

A desk does not stop at the summary. Each claim is cut three ways, using only this study's own assumptions and checks. Nothing here is a new figure.

1. 01 Gossip about gossip

   Observation

   What the study says

   A node tells a random peer everything it knows, including whom it has already told. The history of that gossip is a directed graph. The graph is the input to consensus.

   Model

   What has to hold

   Gossip eventually reaches a supermajority. A lasting partition prevents fame from being decided.

   Falsifier

   What would retire it

   What fraction of members must gossip an event before it can be famous?

2. 02 Virtual voting

   Observation

   What the study says

   Because every node can compute the same graph, each node can calculate how the others would have voted. The paper's claim is that the ballots do not need to cross the network.

   Model

   What has to hold

   Every honest node applies the same deterministic function to the same graph.

   Falsifier

   What would retire it

   Does the application need the paper's fair timestamp, or only a total order?

3. 03 Fairness is ordered by receipt

   Observation

   What the study says

   The paper defines a timestamp from when an event reached a supermajority, and it orders transactions by that time. The fairness claim is this definition, not a general promise about markets.

   Model

   What has to hold

   Gossip eventually reaches a supermajority. A lasting partition prevents fame from being decided.

   Falsifier

   What would retire it

   Does the application need the paper's fair timestamp, or only a total order?

4. 04 The set is permissioned in the core argument

   Observation

   What the study says

   Virtual voting assumes you know who the members are. An open membership race is a different problem. Hedera's later council and permissionless work should not be back-dated into the proof.

   Model

   What has to hold

   Membership is known, and more than two thirds of members follow the protocol.

   Falsifier

   What would retire it

   What fraction of members must gossip an event before it can be famous?

5. 05 Asynchronous Byzantine fault tolerance is the target

   Observation

   What the study says

   The paper argues safety without a leader and without a round timeout as the primary tool. The argument depends on the gossip graph eventually connecting. Partitions still delay the moment a supermajority sees an event.

   Model

   What has to hold

   Gossip eventually reaches a supermajority. A lasting partition prevents fame from being decided.

   Falsifier

   What would retire it

   What fraction of members must gossip an event before it can be famous?

03 Sequence

One action, as an operating tape

1. 01A node creates an event: a payload of transactions plus hashes of two parent events, one from itself and one from a peer.
2. 02It gossips that event, and the events the peer is missing, to a random other member.
3. 03Each member inserts received events into the hashgraph and computes rounds, witnesses and famous witnesses under the paper's rules.
4. 04A famous witness is one that later rounds can all see. Virtual voting decides fame locally.
5. 05Transactions that are ancestors of famous witnesses in the required way receive a consensus timestamp and an order.

04 Load-bearing

The argument, and where a pitch drops it

1. Seeing is the vote

   The cut

   The protocol counts whether a later witness can strongly see an earlier one through enough other members. That graph relation is the ballot. If two honest nodes compute different graphs, they are not in the protocol anymore. Sync of the graph is the honesty of the implementation.

   Why it carries weight

   If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

   Where it is dropped

   A later client, parameter or reward formula is a different object from this paragraph.

2. Fair ordering is not MEV resistance

   The cut

   Ordering by median time of receipt among members is a specific fairness definition. A leader who sequences a public mempool for profit is a different architecture. Do not cite hashgraph as a solution to builder profits on a chain that still has a builder.

   Why it carries weight

   If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

   Where it is dropped

   Fairness here does not mean a user received a good price.

3. Bandwidth is the cost moved, not removed

   The cut

   Virtual voting saves a ballot round. Gossip about gossip still ships the graph. A small permissioned set can do this. A very large set is shuffling a lot of history. The paper's performance claims belong to the set size it has in mind.

   Why it carries weight

   If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

   Where it is dropped

   A permissioned set of gossip peers is load-bearing. Opening the set changes the theorem you are allowed to quote.

05 Register

What has to be true

• Model · Not re-measured

  Membership is known, and more than two thirds of members follow the protocol.

• Stake and threshold · Not re-measured

  Gossip eventually reaches a supermajority. A lasting partition prevents fame from being decided.

• Adversary · Not re-measured

  Every honest node applies the same deterministic function to the same graph.

• Model · Not re-measured

  Payloads inside events are valid under some application rule the consensus layer does not invent.

06 Divergence

What happened after the paper

Hedera built a network around this algorithm, with a governing council and later opening moves that are outside the 2016 paper. Patent and licensing history also sits outside the algorithm. The study here is of the virtual-voting construction, not of a token or a council seat.

A later client, parameter set, or reward formula is a different object. Cite this paper for the mechanism. Cite a primary release for the network. This desk has not re-run the proof.

07 Pre-mortem

What to check before you use the idea

1. Kill test 1Is the member set known, and how does it change?
2. Kill test 2What fraction of members must gossip an event before it can be famous?
3. Kill test 3Does the application need the paper's fair timestamp, or only a total order?
4. Kill test 4Are performance numbers quoted for a small named set or for an open network?
5. 0 of 4 marked on this browser. A mark is a reading note, not a pass, a rating, or a recommendation.

08 Anatomy

The paper, in the order a builder needs

09 Lexicon

Terms, opened into the record

Event

A vertex in the hashgraph: transactions plus hashes of two parents, signed by the member who created it.

Gossip about gossip

Exchanging not only transactions but the history of who talked to whom, so the graph can be reconstructed.

Famous witness

An event that later rounds agree was seen by enough of the set. Fame is decided by virtual vote.

Virtual voting

Computing, from the graph, how members would have voted, so those votes are not sent.

10 Repository

Every linked record on this page

Underlined words open a page that already exists: a concept, a protocol profile, a failure record, or another paper. If a word is not underlined, this desk does not have a record for it.

11 Related

The next papers, as theses

• Avalanche · 2018

  Snowflake to Avalanche: A Novel Metastable Consensus Protocol Family

  A family of consensus protocols that sample the network repeatedly and tip toward one outcome. The 2018 note was pseudonymous. A later write-up adds named co-authors. Avalanche the network is an implementation, not the sample itself.

• Tendermint · 2014

  Tendermint: Consensus without Mining

  A practical Byzantine-fault-tolerant state machine for a known validator set, with instant finality on commit. It became the consensus engine under Cosmos SDK chains. The 2014 note is the origin, not the current CometBFT specification.