HotStuff: QC, highQC, and the three-chain rule

A QC is evidence, not a decorative vote

With n = 3f + 1 replicas, a quorum certificate aggregates 2f + 1 votes for the same proposal and view. Two quorums of that size intersect in at least f + 1 replicas, so the intersection contains at least one correct replica.

highQC preserves the highest known safe tip

Each replica stores the highest-view QC it has verified. A leader carries that memory into its proposal: it does not choose a branch by preference, but extends evidence that replicas can check against their lock.

• The view number orders evidence; it never replaces cryptographic verification.
• The safeNode predicate separates a safe extension from a proposal that merely looks recent.

Three chains separate progress from finality

When three consecutive certified blocks satisfy the required parent-child relation, the oldest block can commit. Pipelining lets prepare, pre-commit, and commit for different blocks coexist without confusing proposal with finality.