Elementary Data Types

A period \(p\) is a 64-bit integer.

A step \(s\) is an 8-bit integer.

Steps are named for clarity and are defined as follows:

The following functions are defined on \(s\):

• \(CommitteeSize(s)\) is a 64-bit integer defined as follows:

  \[ CommitteeSize(s) = \begin{cases} 20 & : s = Propose \\\ 2990 & : s = Soft \\\ 1500 & : s = Cert \\\ 500 & : s = Late \\\ 2400 & : s = Redo \\\ 6000 & : s = Down \\\ 5000 & : \text{otherwise} \end{cases} \]

• \(CommitteeThreshold(s)\) is a 64-bit integer defined as follows:

  \[ CommitteeThreshold(s) = \begin{cases} 0 & : s = Propose \\\ 2267 & : s = Soft \\\ 1112 & : s = Cert \\\ 320 & : s = Late \\\ 1768 & : s = Redo \\\ 4560 & : s = Down \\\ 3838 & : \text{otherwise} \end{cases} \]

A proposal-value is a tuple \(v = (I, p, Digest(e), Hash(Encoding(e)))\) where:

• \(I\) is an address (the “original proposer”),

• \(p\) is a period (the “original period”),

• \(Hash\) is some cryptographic hash function.

The special proposal-value where all fields are the zero-string is called the bottom proposal \(\bot\).