Title: Theory / Unimportant / Compagnie considérée / Near / Block

Name: A finalized block
Definition: A block appearing in the selected chain on its corresponding shard
Page: https://near.org/papers/nightshade/#glossary
Context: Near

Name: An orphaned block
Definition: A block not appearing in the selected chain on its corresponding shard
Page: https://near.org/papers/nightshade/#glossary
Context: Near

Name: The genesis block
Definition: The only initial block, the same for all shards
Page: https://nomicon.io/ChainSpec/Consensus.html
Context: Near
Notation: \(G\)

Page: https://nomicon.io/ChainSpec/Consensus.html
Definition: \(A = prev(\dots(prev(B)\dots)\), for any non-negative number of "prev"
Variables: \(A, B\) blocks
Notation: \(A \le B\)
Name: \(B\) is reachable from \(A\)
Context: Near
Transitive: yes

Page: https://nomicon.io/ChainSpec/Consensus.html
Definition: \(A\le B\) or \(B\le A\)
Variables: \(A, B\) blocks
Notation: \(A \sim B\)
Name: \(\) Near
Transitive: not

Definition: The set of blocks \(B\) such that \(B\le T\)
Page: https://nomicon.io/ChainSpec/Consensus.html
Variables: T block
Context: Near
Notation: chain(T)

Name: The tip of C
Definition: The block B such that \(C=\mathtt{chain}(T)\)
Page: https://nomicon.io/ChainSpec/Consensus.html
Variables: C a chain
Context: Near
Denoted by: T

Name: An epoch
Definition: if \(A<B<C\) and \(A,C \in E\) then \(B\in E\)
Page: https://nomicon.io/ChainSpec/Consensus.html
Context: Near
Conjdef: A set of block E satisfying

Name: The index of E
Definition: \(\mathtt{index}(B(G))=0\)
Page: https://nomicon.io/ChainSpec/Consensus.html
Variables: E an epoch
Context: Near
Definition2: \(\mathtt{index}(pred(B))\) is either \(\mathtt{index}(B)\) or \(\mathtt{index}(B)-1\)
Conjdef: A number such that

Question: When are block proposer determined
Answer: for epoch i, during the last block of epoch i-2
Page: https://nomicon.io/ChainSpec/Consensus.html
Variables: E an epoch
Context: Near

Name: B is final in T
Page: https://nomicon.io/ChainSpec/Consensus.html
Variables: B, T blocks
Context: Near
Notation: \(\mathtt{final}(B, T)\)
Intuition: Once T is generated, its sure B won't be reverted