Uniswap V3のLPポジションから、常に2$\sqrt{x}$の価値を持つポジションを作り出す方法について説明する。Uniswap V3 LPポジションを担保に、いつでもトークンを借りることができることを前提とする。 まずUniswap V3のLP position valueは以下のようになる。 $v(x)=L(2\sqrt{x}-\sqrt{a}-\frac{1}{\sqrt{b}})$ ただし $a$はlowerPrice, $b$はupperPrice、$x$はtoken0のtoken1建ての現在価格である。 この時各トークンの数量は $(token0, token1)=(L(\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{b}}), L({\sqrt{x}}-{\sqrt{a}}))...(0)$

LPポジション価値を以下のように一般化したAMMについて。 value: $v(x)=-ax+b\sqrt{x}-c$ ただし、a>=0, b>=0, c>=0 xはtoken0のtoken1建の価格。 このポジションは以下のようにAsset, Debtを保有する。 ただし(token0, token1)のように記述 asset: $(\frac{b}{2\sqrt{x}}, \frac{b\sqrt{x}}{2})$

Offline swap in Plasma ===== ### Regular step 1. Alice makes StateUpdate to swap ETC with DAI offline. 2. Alice goes offline 3. Bob swaps 1. and his DAI. So, Bob makes 2 StateUpdate. (a). ETH(Alice|Bob) (b). DAI(Bob|Alice) 4. 1.'s deprecate condition is Alice can withdraw (b) or Alice has already spent (b). ### Problem If a user who makes offline swap SU(let say coin A) attempts exit its SU after swap happens, current coin A owner(Bob) should withdraw coin B from Deposit Contract to

# L2 client spec(chamber spec) This client spec of OVM. A whole document is [here](https://hackmd.io/@syuhei/HJRKfUOwr). ### Modules - [clients](https://hackmd.io/3003WCghTou-oXGBcTmuUg?view#L2-Clients): Plasma aggregator and light client implementation, we will add other L2 client here in the future - [ovm](https://github.com/cryptoeconomicslab/wakkanay/tree/master/src/ovm): core OVM implementation - [db](https://github.com/cryptoeconomicslab/wakkanay/tree/master/src/db): general use case da

# OVM Compiler This document describes a practical aspect of [OVM](https://medium.com/plasma-group/introducing-the-ovm-db253287af50) with implementation. [DEMO](https://cryptoeconomicslab.github.io/chamber-lang/) ## Why we need compiler? For instance, plasma construction has StateUpdate and it has Property. If Property size is very large, it's hard to send it to aggregator and smart contract. Secondaly, we want to reduce gas cost of dispute. Claim with big property would take high gas cost f

# L2 and business > Introduction > Hi I’m syuhei. I’m software engineer with 8 years of experience. I've also created my startup which developed Backend as a Service for IoT application in my university days. I think this was one of the reason I entered blockchain. It was hard to maintain the service, so I was studying distributed conmuting such as DHT to build high availability backend. In that time, I knew blockchain.(oh blockchain is amazing but less scalability) After that I worked at som

# How Plasma implementation changed by OVM? [Presentation](https://docs.google.com/presentation/d/1m2tW-JB8j6uHmn0qlYL_WeqpCjahTVPGB-y1Gkp4RlA/edit?usp=sharing) # Outline * About me * History of Plasma implementation * Difficulity of Plasma implementation * Universal Language * How changed Plasma implementation * Conclusion ## Introduction > Hi, I’m going to talking about recent plasma implementation. Title is how Plasma implementation changed. Our Plasma implementation was changed amazingl

# Design idea of universal L2 client These are ideas to make more efficient use of [OVM](https://medium.com/plasma-group/introducing-the-ovm-db253287af50). This architecture enables client more extensible and reduces application specific code. ### Storing and loading local information A quantifier queries local database to fetch local information such as signatures and messages. It's hard to expect how future claims want to query local information. How do we build local information database a

# Road Map 2019-2020 This document is discribing the development roadmap of Plasma Chamber, Cryptoeconomics Lab's Plapps Development Framework. The roadmap includes milestones consisting of each month's **expected implementation tasks** and **deriverables** until testnet launch and mainnet launch. * We will make [Github project board](https://github.com/orgs/cryptoeconomicslab/projects) for each month # Our Goal * Build usable middlewares and applications on layer 2 to produce realworld use

Design pattern of plapp ===== ## Conditional Payment Pattern User can get money in certain condition. * [Fast Finality predicate](https://plasma.build/t/fast-finality-predicate/79) * Payment Channel predicate ### Atomicity Pattern The state transition won't happen when counter stateUpdate isn't included. * Multihop transfer predicate * Payment channel network * Swap predicate * swap inside plasma * swap main chain ans plasma * swap between differrent plasma and plasma ### Extr

Lending Plapp ===== # Overview This document describes an architcture desgin of lending plapps (plasma apps). I outlined the specification referring to [Dharma project](https://www.dharma.io/) functionalities. Special thanks to @ben_chain for review. 1. Collateralizer(Alice) and Lender(Bob) swap their tokens * Alice makes her collateral state with token A and swap the collateral for Bob's token B. * It means that Bob lent token B to Alice 2. Collateral(tokenA) is returned to Alice if