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@@ -90,6 +90,15 @@ proposal's rank in the fork by the fork's length. We use the length
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multiplier to give a preference to longer forks (i.e. longer forks are
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likely to have a higher ranking).
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+The ranking of a fork is always increasing as new blocks are appended.
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+To see this, let $F = (M₁ ⋯ Mₙ)$ be a fork with a finite sequence of blocks $(Mᵢ)$
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+of length $n$. The rank of a fork is calculated as
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+$$ r_F = n ∑ᵢ₌₁ⁿ \t{rank}(Mᵢ) $$
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+Let $F' = F ⊕ (Mₙ₊₁)$ of length $n + 1$ be the fork created by appending
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+the block $Mₙ₊₁$ to $F$. Then we see that
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+$$ r_{F'} > r_F $$
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+since $\t{rank}(M) > 0$ for all $M$.
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+
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## Fork extension
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Since there can be more than one block producer, each node holds a set of known
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zero