$$ \newcommand \DynamicFilterTimeout {\mathrm{DynamicFilterTimeout}} \newcommand \DeadlineTimeout {\mathrm{DeadlineTimeout}} \newcommand \Prop {\mathit{propose}} \newcommand \Soft {\mathit{soft}} \newcommand \Cert {\mathit{cert}} \newcommand \Late {\mathit{late}} \newcommand \Redo {\mathit{redo}} \newcommand \Down {\mathit{down}} \newcommand \Next {\mathit{next}} $$

Habanero Run (Fast Recovery)

Let us now assume a scenario identical to the Japlapeño run, up until the attempt at period \( p = 1 \) to form a \( \Cert \)-Bundle for the pinned value.

In this scenario, a consensus-stalling network partition happens again, which lasts more than 5 minutes (i.e., \( \lambda_f \)).

timeline
    title Habanero Run
    section (r = i, p = 0, 0 <= s <= 1)
        Proposal (s = 0) time = 0                       : Emits proposals for i-th round from selected accounts registered on the node
        Soft Vote (s = 1) time = DynamicTO(p)           : Filters proposals (lowest hash criteria) : Soft vote on the best proposal for round i
    section (r = i, p = 0, s >= 2) Network partition K begins
        Certification (s = 2) time = DeadlineTO(p=0)    : Certification vote fails, no Committe Threshold is reached
        Recovery (s > 3) time > DeadlineTO(p=0)         : Next and Fast Recovery votes triggered : No Next bundle is observed
    section (r = i, p = 0, s >= 3) Network partition K ends
        Recovery (s > 3) time > DeadlineTO(p=0)         : Next Bundle observed, new period begins
    section (r = i, p = 1, s = [253, 254, 255])
        Fast Recovery (s = 253) time = lambda_f         : Late step fails
        Fast Recovery (s = 254)                         : Redo step fails
        Fast Recovery (s = 255)                         : Down Bundle observed, new period begins
    section (r = i, p = 2, 0 <= s <= 2)
        Proposal (s = 0) time = 0                       : Emits proposals for i-th round from selected accounts registered on the node
        Soft Vote (s = 1) time = DynamicTO(p=2)         : Filters proposals (lowest hash criteria) : Soft vote on the best proposal for round i
        Certification (s = 2) time < DeadlineTO(p=2)    : Certification vote of a pinned value
                                                        : Appended i-th block to the Ledger
                                                        : State deltas applied
                                                        : Transaction pool purged

Run

Let us assume the network conditions are those described in the initial context.

In addition to the initial context:

• The network successfully performed \( \Prop \) and \( \Soft \) steps for round \( r \),

• During the \( \Cert \) step, before the block commitment, the network experiences a partitioning \( K \) (as described in the Jalapeno run),

• Players reach \( \DeadlineTimeout(p = 0) \) without a committable block proposal (that is, no \( \Cert \)-Bundle supporting any proposal-value has been observed).

Fast Recovery

Under these conditions, a \( \Cert \)-Bundle is not formed and the protocol enters in partition recovery mode.

Now, after connections are reestablished, a \( \Next \)-Bundle for a new period \( p = 1 \) is observed, and a fast recovery is about to take place (when the node’s clock is equal to \( \lambda_f \)).

In this scenario, however, differently from the Jalapeño run, most players have lost the previously observed pinned value, or have since seen \( \Soft \)-Bundle for different values. Therefore, no consensus on a bundle going into the period \( p = 2 \) certification is possible.

In this case, after failing to form \( \Late \) and \( \Redo \) bundles, a \( \Down \)-Bundle is observed by a majority of players (an “agree to disagree” with value \( \bot \)).

Players move into a period \( p = 2 \), this time with no “carry over” information from the previous consensus attempt.

In this scenario, the whole protocol is rerun (a reproposal ensues). The rest of the scenario is similar to the Vanilla run, save for different timeout values for \( DynamicFilterTimeout(p = 2) \) and \( DeadlineTimeout(p = 2) \), the protocol goes over \( \Prop \), \( \Soft \) and \( \Cert \) steps in the same fashion.

However, in this case, the network partition has been solved, so a block commitment ensues before \( \DeadlineTimeout(p = 2) \).