# kaal:claim:5225296-019

**Claim.** 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.

**Type.** condition  **Support.** evidenced

**Holds when.**

- fewer than n/3 of n nodes faulty

**Source quote.**

> 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

**From.** Wulf A. Kaal, *Cryptographic Foundations and Interdisciplinary Dimensions of the Secure Proof of Stake (SPoS) Conse* (2025), Security Against Byzantine Faults

**Cite as.** Wulf A. Kaal, Cryptographic Foundations and Interdisciplinary Dimensions of the Secure Proof of Stake (SPoS) Conse (2025). SSRN: https://ssrn.com/abstract=5225296

**Verify.** sha256 of source PDF `b2fec675d906334ad67e13b2d97261dc31e38061022867eb3f9ceadd95f4878d` at https://raw.githubusercontent.com/wulfkaal/Academic-Papers/main/papers/pdf/Kaal%20-%202025%20-%20Cryptographic%20Foundations%20and%20Interdisciplinary%20Dimensions%20of%20the%20Secure%20Proof%20of%20Stake%20%28SPoS%29%20Conse.pdf

**Topics.** consensus-and-security

**Keywords.** byzantine-fault-tolerance, pbft, one-third-threshold, liveness-and-safety

**Canonical form.** This markdown file is the canonical hashed representation of the claim. Its sha256 is the content hash used for attestation.