# Fraud Tax Definition

## Definitions[](https://)

$g \in G$: set of grants
$u \in U$: set of users
$c \in C$: set of contributions

$C$: All contributions
$C^*$: Contributions coming from non-sybil users (or modified contribution graph with suspected sybils removed)

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The CLR matching grant is a mapping between a specific grant, parametrized by a contribution graph, towards a real number:

$CLR(g\in G; C) \to \mathbb{R}$

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The max CLR matching payout of a grant is defined as:

$p(g; C, C^*) := max[CLR(g; C), CLR(g; C^*)]$

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The fraud tax is defined as the sum of all max CLR matching payouts per grant, subtracted by the total CLR match on the original contributions data (or the total matching pool pot).

$T := \sum_{g \in G} p(g; C, C^*) - \sum CLR(g; C)$

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The Fraud Tax Rate is defined as

$T\% := \frac{T}{TotalCLR}$