{
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 "@type": "DefinedTerm",
 "@id": "https://wulfkaal.github.io/entities/byzantine-fault-tolerance",
 "identifier": "kaal:entity:byzantine-fault-tolerance",
 "name": "Byzantine fault tolerance",
 "termCode": "byzantine-fault-tolerance",
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 "author": {
  "@type": "Person",
  "name": "Wulf A. Kaal",
  "identifier": "https://orcid.org/0000-0003-0757-275X"
 },
 "dateModified": "2026-07-29",
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  {
   "@type": "Claim",
   "@id": "https://wulfkaal.github.io/claims/3125827-008",
   "identifier": "kaal:claim:3125827-008",
   "text": "Given that Byzantine faults are inevitable in a distributed system, the known impossibility results force any consensus protocol to hedge: it can promise only a probability of finality and security, and that probability is inversely proportional to liveness and speed.",
   "abstract": "Given the inevitable possibility of Byzantine faults in a distributed system, such results require any protocol to hedge, promising only a probability of finality and security inversely proportional to liveness and speed.",
   "citation": "Craig Calcaterra, Wulf A. Kaal, Secure Proof of Stake Protocol (2018). SSRN: https://ssrn.com/abstract=3125827",
   "datePublished": "2018",
   "claim_type": "condition",
   "confidence": "evidenced",
   "is_failure_mode": false,
   "scope_conditions": [
    "asynchronous distributed networks",
    "presence of Byzantine faults"
   ],
   "source_pdf_sha256": "598d9bd95e4af7a0a35328677c6bfc069f69f2e32c30c720b3a0be98a23a40cb",
   "status": "current"
  },
  {
   "@type": "Claim",
   "@id": "https://wulfkaal.github.io/claims/3125827-012",
   "identifier": "kaal:claim:3125827-012",
   "text": "No consensus protocol can guard against Byzantine faults when a single transaction is worth more than the promise of all future fees for the entire platform, because in that case a party can profitably bribe the whole node set to destroy the chain's own integrity.",
   "abstract": "No protocol can guard against Byzantine faults if a transaction is more valuable than the promise of all future fees for the entire platform; in this case a party could bribe the entire set of nodes (or 51%)",
   "citation": "Craig Calcaterra, Wulf A. Kaal, Secure Proof of Stake Protocol (2018). SSRN: https://ssrn.com/abstract=3125827",
   "datePublished": "2018",
   "claim_type": "failure",
   "confidence": "argued",
   "is_failure_mode": true,
   "scope_conditions": [
    "a single transaction whose value exceeds the present value of all future platform fees"
   ],
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   "@type": "Claim",
   "@id": "https://wulfkaal.github.io/claims/3125827-029",
   "identifier": "kaal:claim:3125827-029",
   "text": "If a Byzantine producer equivocates during a network partition and wins validation pools in separate subnets, the fork is not permanent: once connectivity is restored the next honest producer points to a previous block, and with 51% honest producers the Byzantine fork is eventually orphaned because honest producers outproduce it.",
   "abstract": "The next honest producer would point to a previous block and all Byzantine forks would be invalidated. If there are 51% honest producers the Byzantine fork would eventually be orphaned, since honest producers will outproduce the Byzantine producers",
   "citation": "Craig Calcaterra, Wulf A. Kaal, Secure Proof of Stake Protocol (2018). SSRN: https://ssrn.com/abstract=3125827",
   "datePublished": "2018",
   "claim_type": "mechanism",
   "confidence": "argued",
   "is_failure_mode": false,
   "scope_conditions": [
    "at least 51% honest producers",
    "network connectivity is eventually restored"
   ],
   "source_pdf_sha256": "598d9bd95e4af7a0a35328677c6bfc069f69f2e32c30c720b3a0be98a23a40cb",
   "status": "current"
  },
  {
   "@type": "Claim",
   "@id": "https://wulfkaal.github.io/claims/5225296-019",
   "identifier": "kaal:claim:5225296-019",
   "text": "SPoS inherits PBFT's stability threshold: the three-phase pre-prepare, prepare, and commit protocol secures agreement despite Byzantine behavior, but formal analysis proves stability only while fewer than one third of nodes are faulty.",
   "abstract": "PBFT's three-phase protocol—pre-prepare, prepare, and commit—ensures agreement despite Byzantine behavior, with formal threshold analysis proving stability when fewer than n/3 of n nodes are faulty",
   "citation": "Wulf A. Kaal, Cryptographic Foundations and Interdisciplinary Dimensions of the Secure Proof of Stake (SPoS) Conse (2025). SSRN: https://ssrn.com/abstract=5225296",
   "datePublished": "2025",
   "claim_type": "condition",
   "confidence": "evidenced",
   "is_failure_mode": false,
   "scope_conditions": [
    "fewer than n/3 of n nodes faulty"
   ],
   "source_pdf_sha256": "b2fec675d906334ad67e13b2d97261dc31e38061022867eb3f9ceadd95f4878d",
   "status": "current"
  }
 ],
 "description": "4 claims in the published works of Wulf A. Kaal carry the concept tag 'byzantine-fault-tolerance'. Derived node: a roster, not an adjudicated definition."
}