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‎components/StakingCapBar.tsx

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import React, { useState } from "react";
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import React from "react";
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const StakingCapBar = () => {
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const [maxRewardRate, setMaxRewardRate] = useState(10);
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interface StakingCapBarProps {
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totalLength?: number;
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height?: number;
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barColor?: string;
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secondBarColor?: string;
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backgroundColor?: string;
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fillPercentage: number;
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secondFillPercentage: number;
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}
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const barWidth = 300;
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const barHeight = 30;
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export default function StakingCapBar({
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totalLength = 300,
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height = 80,
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barColor = "bg-blue-500",
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secondBarColor = "bg-green-500",
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backgroundColor = "bg-gray-200",
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fillPercentage,
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secondFillPercentage,
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}: StakingCapBarProps) {
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// Ensure fillPercentages are between 0 and 100
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const clampedFillPercentage = Math.min(100, Math.max(0, fillPercentage));
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const clampedSecondFillPercentage = Math.min(
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100 - clampedFillPercentage,
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Math.max(0, secondFillPercentage)
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);
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return (
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<div className="flex flex-col items-start p-4 max-w-md">
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<h2 className="text-xl font-bold mb-2">Example:</h2>
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<div className="mb-4 w-full">
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<label
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htmlFor="rewardRateSlider"
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className="block text-sm font-medium text-gray-700 mb-1"
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>
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Max Reward Rate: {maxRewardRate}%
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</label>
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<input
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type="range"
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id="rewardRateSlider"
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min="0"
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max="100"
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value={maxRewardRate}
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onChange={(e) => setMaxRewardRate(Number(e.target.value))}
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className="w-full h-2 bg-gray-200 rounded-lg appearance-none cursor-pointer"
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/>
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</div>
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<div className="relative w-full h-8 bg-gray-200 rounded">
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<div className="flex flex-col items-center space-y-6 p-6 bg-gray-100 rounded-lg">
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<h2 className="text-2xl font-bold">Staking Cap Bar</h2>
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<div
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className="w-full max-w-sm bg-white p-4 rounded-lg shadow-inner"
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style={{ width: `${totalLength}px` }}
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>
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<div
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className="absolute top-0 left-0 h-full bg-blue-500 rounded"
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style={{ width: `${maxRewardRate}%` }}
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></div>
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<div className="absolute top-0 left-0 w-full h-full flex items-center justify-between px-2">
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<span className="text-sm font-semibold">0%</span>
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<span className="text-sm font-semibold">100%</span>
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className={`${backgroundColor} rounded overflow-hidden border border-gray-300`}
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style={{ height: `${height}px` }}
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role="progressbar"
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aria-valuenow={clampedFillPercentage + clampedSecondFillPercentage}
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aria-valuemin={0}
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aria-valuemax={100}
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>
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<div className="flex h-full">
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<div
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className={`${barColor} h-full transition-all duration-300 ease-in-out`}
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style={{ width: `${clampedFillPercentage}%` }}
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></div>
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<div
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className={`${secondBarColor} h-full transition-all duration-300 ease-in-out`}
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style={{ width: `${clampedSecondFillPercentage}%` }}
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></div>
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</div>
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</div>
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</div>
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<p className="mt-2 text-sm text-gray-600">
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Max Reward Rate = {maxRewardRate}%
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</p>
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<div className="text-center">
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<p className="text-lg font-semibold text-gray-700">
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First Fill: {clampedFillPercentage}%
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</p>
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<p className="text-lg font-semibold text-gray-700">
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Second Fill: {clampedSecondFillPercentage}%
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</p>
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<p className="text-lg font-semibold text-gray-700">
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Total Fill: {clampedFillPercentage + clampedSecondFillPercentage}%
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</p>
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<p className="text-sm text-gray-600">Total Length: {totalLength}px</p>
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</div>
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</div>
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);
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};
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export default StakingCapBar;
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}

‎pages/home/pyth-token/oracle-integrity-staking.mdx

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## Design Principles
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OIS's economic design focuses on awarding and penalizing Stakers over the primary dimension of data accuracy.
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OIS's economic design focuses on awarding and penalizing Stakers over the primary dimension of data accuracy.
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Stakers receive rewards from an open-ended pool for helping to ensure data quality. They will also have their stake slashed as a penalty for failing to maintain data accuracy.
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The core design principles behind OIS include the following:
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## Implementation
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OIS implements the principle above through the following structure:
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OIS implements the principle above through the following structure:
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1. OIS is subject to the same 7-day epoch as Governance voting. All parameters used in the OIS protocol are captured at each start of the epoch on Thursdays at 0:00 UTC and remain constant until the end of the epoch. Staking into OIS is also subject to warmup and cooldown period prior and post epoch respectively.
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2. Each publisher is programmatically assigned a staking pool where they can self-stake and to which other stakers can delegate
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- The staking pool assigned to each publisher covers all price feeds/symbols they publish.
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- Each staking pool has a soft cap. This soft cap dynamically expands and shrinks given the number of symbols published by the assigned publisher.
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- Price feeds with a low number of publishers contribute less to the cap's expansion.
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- Staking into the pool can exceed the soft cap. However no rewards are paid nor penalties are levied on the excess amount.
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- The OIS protocol prioritizes self-stake attributed to the **publisher's stake** when distributing rewards to the publisher's pool.
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- All staking pools charge the same delegation fee for stakers who are delating stake to one or many pools.
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- The staking pool assigned to each publisher covers all price feeds/symbols they publish.
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- Each staking pool has a soft cap. This soft cap dynamically expands and shrinks given the number of symbols published by the assigned publisher.
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- Price feeds with a low number of publishers contribute less to the cap's expansion.
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- Staking into the pool can exceed the soft cap. However no rewards are paid nor penalties are levied on the excess amount.
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- The OIS protocol prioritizes self-stake attributed to the **publisher's stake** when distributing rewards to the publisher's pool.
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- All staking pools charge the same delegation fee for stakers who are delating stake to one or many pools.
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3. Each pool has a maximum reward rate per epoch, which applies only to the staked amount within the soft cap.
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4. The total amount of rewards paid to all pools is bound by the same cap relative to the amount of rewards available to the OIS protocol.
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5. Slashing of stake has a hard cap and only impacts pools that assigned to publishers responsible for the poor data quality. Both self-stakers and delegators are also slashed proportionally to their staked amount in the impacted pools.
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5. Slashing of stake has a hard cap and only impacts pools that assigned to publishers responsible for the poor data quality. Both self-stakers and delegators are also slashed proportionally to their staked amount in the impacted pools.

‎pages/home/pyth-token/oracle-integrity-staking/_meta.json

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{
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"mathematical-representation": "Mathematical Representation",
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"examples": "Examples"
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}

‎pages/home/pyth-token/oracle-integrity-staking/examples.mdx

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import StakingCapBar from '@/components/StakingCapBar'
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import StakingCapBar from "@/components/StakingCapBar";
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# Examples(WIP)
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<StakingCapBar fillPercentage={50} secondFillPercentage={20} />
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### Example 1:Only Publisher State
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\text{Total Amount eligible for Reward} \quad{R_a} = min({S}_p, {C}_p) = min(500, 100) = 100
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$$
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$$
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\text{Reward Rate} \quad{r} = 10\%
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$$
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$$
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\text{Delegator Reward} \quad{R^d_p} = {R_p} - {R^p_p} = 10 - 10 = 0
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$$
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$$

‎pages/home/pyth-token/oracle-integrity-staking/mathematical-representation.mdx

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# Mathematical Representation
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This section outlines the mathematical representation of the Oracle Integrity Staking (OIS) protocol.
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As explained in the [implementation](./implementation.mdx) section, every publisher is assigned a staking pool where they can self-stake and to which other stakers can delegate.
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## Pool Cap
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The **pool cap** is calculated as follows:
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$$
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\large{\text{Pool Cap}: {\bold{C_p}} = M \cdot \sum_{s \in \text{Symbols\_p}} \frac{1}{\max(n_s, Z)}}
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$$
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Where:
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- $M$ is a constant parameter representing the target stake per symbol.
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- $\text{Symbols\_p}$ is the number of symbols published by the publisher $p$.
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- $n_s$ is the number of elements in Symbols_p , or $n_s$ = $|\text{Symbols\_p}|$
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- $Z$ is a constant parameter to control cap contribution from symbols with a low number of publishers.
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This formula actually ensures that symbols with a lower number of publishers contribute more to the overall cap, while symbols with a higher number of publishers contribute less. This is because the contribution of each symbol is inversely proportional to the number of publishers (or Z, whichever is larger).
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## Reward
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The reward $R_p$ paid to each pool is calculated as follows:
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$$
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\large{R_p = y \cdot \min(S_p, C_p)}
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$$
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Where:
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- $y$ is the cap to the rate of rewards for any pool.
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- $S_p$ be the stake assigned to the publisher p pool , made of self-staked amount $S^{p}_{p}$ and delegated stake $S^{d}_{p}$ , or $S_{p} = S^{p}_{p} + S^{d}_{p}$.
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- $C_p$ be the stake cap for the pool assigned to publisher p.
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The reward is capped at the pool cap, $C_p$, to ensure that publishers and delegators are not over-rewarded. (I don't this this is necessary to mention, but it is a good sanity check)
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The total amount of rewards paid to all pools is bound the the same cap relative to the amount of rewards available to the OIS protocol.
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$$
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\large{\sum_{p \in \text{Publishers}} R_p \leq y \cdot \min(NumSymbols \cdot M, \sum_{p=1}^{P} S_p)}
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$$
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Where:
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- $NumSymbols$ is the total number of symbols in the system.
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- $P$ is the total number of publishers in the system.
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Whereas the reward component relative to the amount self-staked by the publisher $p$ is defined as:
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$$
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\large{R^{p}_{p} = y \cdot \min(S^p_p, C_p) = R_p - R^d_p}
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$$
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Where:
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- $R^d_p$ is the reward component relative to the amount delegated to the publisher $p$.
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## Slashing
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Slashing is an important aspect of the OIS protocol to ensure the integrity of the system.
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The slashed amount for each pool is calculated as follows:
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$$
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\large{SL_p = z \cdot S_p = z \cdot (S^{p}_{p} + S^{d}_{p})}
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$$
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Where:
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- $SL_p$ is the slashed amount for the publisher $p$ pool.
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- $z$ is the slashing rate.
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- $S_p$ is the stake assigned to the publisher $p$ pool , made of self-staked amount $S^{p}_{p}$ and delegated stake $S^{d}_{p}$ , or $S_{p} = S^{p}_{p} + S^{d}_{p}$.
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Here $SL_p$ is uniformly allocated to both the self-staking publisher and delegators in the pool, pro-rata to their respective stake.
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Subsequently, the rewards received by a publisher and delegators into a pool, net of any slashed amounts can be expressed as below:
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$$
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\large{\Pi^p_p = ( R^p_p + f \cdot R^d_p ) - z \cdot S^p_p}
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$$
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$$
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\large{\Pi^d_p = R^d_p - ( f \cdot R^d_p + z \cdot S^d_p )}
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$$
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Where:
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- $\Pi^p_p$ is the net reward received by the publisher $p$ after slashing.
100+
- $\Pi^d_p$ is the net reward received by the delegator $p$ after slashing.
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- $f$ is the delegation fee charged by the publisher.
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- $z$ is the slashing rate.
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- $S^p_p$ is the amount self-staked by the publisher $p$.
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- $S^d_p$ is the amount delegated to the publisher $p$.

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