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further latex fixes
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XLS-0065-single-asset-vault/README.md

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@@ -246,7 +246,7 @@ The calculation depends on whether the vault is empty.
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- **Initial Deposit**: For the first deposit into an empty vault, shares are calculated using a scaling factor, $\sigma = 10^{\text{Scale}}$, to properly represent fractional assets as whole numbers.
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$$\Delta_{shares} = \Delta_{assets} \times \sigma$$
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- **Subsequent Deposits**: For all other deposits, shares are calculated proportionally using the deposit NAV ($\Gamma_{assets} - \Omega$). The resulting $\Delta_{shares}$ value is **rounded down** to the nearest integer.
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- **Subsequent Deposits**: For all other deposits, shares are calculated proportionally using the deposit NAV. The resulting $\Delta_{shares}$ value is **rounded down** to the nearest integer.
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$$\Delta_{shares} = \frac{\Delta_{assets} \times \Gamma_{shares}}{\Gamma_{assets} - \Omega}$$
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Because the share amount is rounded down, the actual assets taken from the depositor ($\Delta_{assets'}$) are recalculated.
@@ -266,7 +266,7 @@ The redeem function calculates the asset payout for a user burning a specific nu
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**Calculation Logic**
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The amount of assets a user receives is calculated by finding the proportional value of their shares relative to the vault's withdrawal NAV ($\Gamma_{assets} - \Omega - \iota$), which accounts for both unrealized interest and unrealized loss.
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The amount of assets a user receives is calculated by finding the proportional value of their shares relative to the vault's withdrawal NAV, which accounts for both unrealized interest and unrealized loss.
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$$\Delta_{assets} = \frac{\Delta_{shares} \times (\Gamma_{assets} - \Omega - \iota)}{\Gamma_{shares}}$$
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@@ -281,13 +281,13 @@ The vault's totals are reduced after the redemption.
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The withdraw function handles a request for a specific amount of assets, which involves a two-step process to determine the final payout.
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First, the requested asset amount ($\Delta_{assets\\_requested}$) is converted into the equivalent number of shares to burn, based on the vault's withdrawal NAV ($\Gamma_{assets} - \Omega - \iota$).
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First, the requested asset amount is converted into the equivalent number of shares to burn, based on the vault's withdrawal NAV.
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$$\Delta_{shares} = \frac{\Delta_{assets\\_requested} \times \Gamma_{shares}}{(\Gamma_{assets} - \Omega - \iota)}$$
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This calculated $\Delta_{shares}$ amount is **rounded down (floor)** to the nearest whole number.
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Next, the floored number of shares from Step 1 is used to calculate the final asset payout ($\Delta_{assets\\_out}$), using the same logic as a redemption.
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Next, the floored number of shares from Step 1 is used to calculate the final asset payout using the same logic as a redemption.
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$$\Delta_{assets\\_out} = \frac{\Delta_{shares} \times (\Gamma_{assets} - \Omega - \iota)}{\Gamma_{shares}}$$
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