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@@ -52,6 +52,127 @@ tracked.
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> concluded without access to the vesting information and/or the shared
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> secret address.
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+### Vesting formulas
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+
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+Let $E, S, V, C, T$ be the vesting configuration parameters as defined
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+in [Vesting Configuration](model.md#vesting-configuration).
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+
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+Let $t₀ = \t{BlockWindow} ∈ 𝔽ₚ$ be the current blockwindow as defined
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+in [Blockwindow](model.md#blockwindow).
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+
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+Let $Bv ∈ ℕ₆₄$ be the burned coin.
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+
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+The core formula to compute amounts corresponding to the current block
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+window is:
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+
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+$$ \begin{aligned}
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+CurrentBlockwindow = CondSelect(BlockwindowCond, t₀, E); \\
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+BlockwindowsPassed = CurrentBlockwindow - S; \\
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+Available = (BlockwindowsPassed * V) + C; \\
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+Withdrawn = T - Bv; \\
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+WithdrawCoinValue = Available - Withdrawn; \\
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+VestingChangeValue = T - (Withdrawn + WithdrawCoinValue);
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+\end{aligned} $$
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+
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+The vesting schedule model says that any blockwindow $t$ where
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+$S <= t <= E$, the total amount that should have been unlocked is:
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+
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+$$ \begin{aligned}
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+Available(t) = (t - S) * V + C;
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+\end{aligned} $$
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+
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+And we know from the vest proof's constraint that $T = (E-S) * V + C$,
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+so $Available(E) = T$. The schedule is linear between $S$ and $E$ with
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+a cliff C at the start.
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+
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+The burned vested coin has value $Bv$ which represents the remaining
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+balance in the vested coin. Initially (right after vest) $Bv = T$.
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+After each withdrawal it shrinks.
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+
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+So "total withdrawn so far" is $T - Bv$ and the formula computes how
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+much new value the vestee can take:
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+
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+$$ \begin{aligned}
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+WithdrawCoinValue = Available - (T - Bv) = Available - T + Bv; \\
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+VestingChangeValue = Bv - WithdrawCoinValue;
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+\end{aligned} $$
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+
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+Concrete example:
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+
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+Let:
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+
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+$$ \begin{aligned}
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+T = 1000; \\
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+C = 100; \\
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+S = 10; \\
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+E = 20; \\
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+V = 90; \\
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+(20 - 10) * 90 + 100 = 1000;
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+\end{aligned} $$
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+
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+First withdrawal at $t = 12$ with $Bv = 100$ as the initial vested coin:
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+
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+$$ \begin{aligned}
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+Available = (12 - 10) * 90 + 100 = 280; \\
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+Withdrawn = 1000 - 1000 = 0; \\
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+WithdrawCoinValue = 280 - 0 = 280; \\
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+VestingChangeValue = 1000 - 280 = 720;
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+\end{aligned} $$
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+
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+Conservation: $280 + 720 = 1000 = Bv$
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+
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+Second withdrawal at $t = 15$ with $Bv = 720$ from previous change coin:
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+
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+$$ \begin{aligned}
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+Available = (15 - 10) * 90 + 100 = 550; \\
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+Withdrawn = 1000 - 720 = 280; \\
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+WithdrawCoinValue = 550 - 280 = 270; \\
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+VestingChangeValue = 720 - 270 = 450;
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+\end{aligned} $$
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+
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+Conservation: $270 + 450 = 720 = Bv$
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+
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+Cumulative withdrawn: $280 + 270 = 550 = Available(15)$
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+
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+Final withdrawal at $t = 20$ (end) with $Bv = 450$ from previous change
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+coin:
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+
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+$$ \begin{aligned}
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+Available = (20 - 10) * 90 + 100 = 1000; \\
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+Withdrawn = 1000 - 450 = 550; \\
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+WithdrawCoinValue = 1000 - 550 = 450; \\
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+VestingChangeValue = 450 - 450 = 0;
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+\end{aligned} $$
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+
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+Cumulative: $280 + 270 + 450 = 1000 = T$
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+
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+Expanding $VestingChangeValue$:
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+
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+$$ \begin{aligned}
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+VestingChangeValue = Bv - WithdrawCoinValue; \\
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+VestingChangeValue = Bv - (Available - T + Bv); \\
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+VestingChangeValue = T - Available;
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+\end{aligned} $$
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+
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+at $t = 12$, $change=1000-280=720$
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+
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+at $t = 15$, $change=1000-550=450$
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+
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+at $t = 20$, $change=1000-1000=0$
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+
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+^ This means $WithdrawCoinValue = Bv - (T - Available) = Bv -
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+VestingChangeValue$ which is just the difference between what the coin
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+held and what must remain locked.
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+
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+We can compute $VestingChangeValue = T - Available$ then derive
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+$WithdrawCoinValue = Bv - VestingChangeValue$.
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+
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+Proof simplification:
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+$$ \begin{aligned}
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+VestingChangeValue = BaseSub(T, Available); \\
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+WithdrawCoinValue = BaseSub(Bv, VestingChangeValue)
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+\end{aligned} $$
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+
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## Forfeit
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With this call, a vesting authority is able to forfeit a specific
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skoupidi