$$ \newcommand \Cert {\mathit{cert}} \newcommand \Soft {\mathit{soft}} \newcommand \Vote {\mathrm{Vote}} \newcommand \Bundle {\mathrm{Bundle}} \newcommand \Proposal {\mathrm{Proposal}} $$

Certifying

On observing that some proposal-value \( v \) is committable for its current round \( r \), and some period \( p’ \geq p \) (its current period), if \( s \leq \Cert \), then the player broadcasts* \( \Vote(I, r, p, \Cert, v) \). (It can be shown that this occurs either after a proposal is received or a soft-vote, which can be part of a bundle, is received.)

For a detailed overview of how the certification step may be implemented, refer to the Algorand ABFT non-normative section.

In other words, if observing a soft-vote causes a proposal-value to become committable,

$$ N(S, L, \Vote(I, r, p, \Soft, v)) = (S’, L, (\ldots, \Vote(I, r, p, \Cert, v))); $$

while if observing a bundle causes a proposal-value to become committable,

$$ N(S, L, \Bundle(r, p, \Soft, v)) = (S’, L, (\ldots, \Vote(I, r, p, \Cert, v))); $$

and if observing a proposal causes a proposal-value to become committable,

$$ N(S, L, \Proposal(v)) = (S’, L, (\ldots, \Vote(I, r, p, \Cert, v))); $$

as long as \( s \leq \Cert \).