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'EPISTEMOLOGY I The Theory of Knowledge'
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Interior Design Thesis Exhibition/ นิทรรศการโครงการศิลปนิพนธ์ ของนักศึกษาชั้นปีที่ 4 สาขาออกเเบบภายใน วิทยาลัยการออกเเบบ มหาวิทยาลัยรังสิต
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EPISTEMOLOGY way of thinking is powered by validated human knowledge, truth and beliefs. This philosophy helped and allowed our graduates to have the freedom of creativity, to wonder beyond the horizon while respecting the importance of practicality, functionality and positive impact on the community, selected industry and most importantly the environment.
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Grab and Go 2021 Thesis Art Exhibition will be showcase at Samyan Mitrtown Hall, 5th floor from July 3th-11th, 2021 or simply scan the QR code to virtually unveiled the exhibition. For more information, please visit …
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📜 [專欄新文章] Uniswap v3 Features Explained in Depth

✍️ 田少谷 Shao

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

Once again the game-changing DEX 🦄 👑

Image source: https://uniswap.org/blog/uniswap-v3/

Outline

0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion

0. Intro

The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥

While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.

Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅

Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊

If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏

There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!

1. Uniswap & AMM recap

Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.

Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.

Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:

AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.

Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².

Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.

In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP

¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity

² the range is in fact [-∞,∞], while a price in most cases won’t be negative

³ AMM of constant sum does not have price slippage

2. Tick

The whole innovation of Uniswap v3 starts from ticks.

For those unfamiliar with what is a tick:

Source: https://www.investopedia.com/terms/t/tick.asp

By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:

The price range of each tick is predefined by the system instead of being proposed by users.

Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.

Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.

With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯

So, how is the price range of a tick decided?

This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.

The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.

Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.

However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.

This is how price ranges of ticks are decided⁴:

Image source: https://uniswap.org/whitepaper-v3.pdf

With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.

As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.

For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.

p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001

See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?

Image source: https://tenor.com/view/coin-master-cool-gif-19748052

But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?

Price range: max & min

To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.

Image source: https://uniswap.org/whitepaper-v3.pdf

The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.

24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:

1.0001 ^ (2¹⁸) = 242,214,459,604.341

1.0001 ^ -(2¹⁷) = 0.000002031888943

I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌

⁴ For implementation concern, however, a square root is added to both sides of the equation.

How about finding out which tick does a price belong to?

Tick index from price

The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:

Image source: https://www.codecogs.com/latex/eqneditor.php

Let’s try this out, say we wanna find out the tick index of 1000000.

Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm

Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!

⁵ This formula is also slightly modified to fit the real implementation usage.

3. Concentrated liquidity

Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.

Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.

As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!

Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/

Mmm… examples are always helpful for abstract descriptions 😂

Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].

If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.

The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.

However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).

We can observe the following two points from the above example:

Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.

√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.

What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!

Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!

Image source: https://uniswap.org/blog/uniswap-v3/

It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵

⁶ Thanks to Yenwen Feng for the information.

4. Range orders: reversible limit orders

As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:

current price < the targeted price range

current price > the targeted price range

current price belongs to the targeted price range

The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.

The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).

There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!

In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.

Range orders

To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.

The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.

For the price of X to go up, y has to increase and x decrease.

With this pricing mechanism in mind, it’s example time!

Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).

The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.

The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.

If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.

Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.

What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].

This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.

…wut? 🤔

Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!

What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.

The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.

Image source: https://uniswap.org/blog/uniswap-v3/

Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.

To wrap up such an interesting feature, we know that:

Only one token is required for range orders.

Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯

I will be discussing more the impacts of v3 in 5. Impacts of v3.

⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.

Reversible limit orders

As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.

We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].

Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.

The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.

As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:

When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸

When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸

A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!

⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.

5. Impacts of v3

Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:

Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.

The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.

LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏

In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.

After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔

Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!

6. Conclusion

That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂

There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅

If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!

Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟

Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

👏 歡迎轉載分享鼓掌

臺灣吧將動畫臺灣史 228影片 重新英文配音，
歡迎分享給你身邊世界各地的朋友。
＿
　
在covid19疫情中，
許多人都在問「台灣怎麼抗疫的？」
當世界各地因宵禁和封城引發抗議，疫情卻仍持續升溫時，
臺灣透過公開透明的資訊、民眾與政府的互信合作、
還有精實有經驗的醫療系統，在風雨飄搖的2020，
讓人民維持正常生活、讓經濟依然穩健成長。

During the COVID-19 pandemic, many wonder “How does Taiwan beat COVID-19 successfully ?”

Though many countries are striving to keep its people safe from the pandemic by implementing lockdowns, curfews and facility closures, voices of protest constantly appear.

In Taiwan, on the other hand, people work with the government harmonically during this difficult time. Taiwanese government conducts effective strategies concerning the pandemic and shares the information with the public. Furthermore, thanks to an advanced healthcare system, citizens enjoy prosperity and continue to live normal lives.

﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏
▞ 臺灣的民主化成就，並非一蹴可幾 ▚
﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋
許多國家從專制邁向民主的過程，都曾歷經流血衝突
在74年前的今天，臺灣也同樣經歷一場血腥鎮壓。
　
在二次大戰結束後，日本戰敗
原本在日本人統治之下的臺灣
被中華民國接收，島民們一下子從
戰敗者變成戰勝者。
　
中華民國政府接收臺灣後，卻讓
官員貪腐、通貨膨脹、經濟倒退、歧視打壓等問題
越演越烈。衝突在2/28爆發。
　
這場運動造成大量傷亡，
卻沒有辦法阻止極權統治停下腳步。
1949年，政府甚至展開了長達38年的戒嚴，
許多台灣人在戒嚴期間遭受
不明原因的白色恐怖，從此人間蒸發。
　
直到1987年解嚴，
並歷經各種針對體制的衝撞與抗爭，
臺灣才漸漸轉型成為大家看到的民主多元國家。

- the Price of Democracy -
The harmonious relationship between the government and the people has lasted, but Rome wasn’t built in one day; Taiwan’s democratic achievement did not come easy. The shift from autocracy to democracy came with bloody fights.

With Japan’s defeat after World War II, the Republic of China government began exercising jurisdiction over Taiwan and reinforced the oppression to secure authorities on the island. Taiwan was plagued with official corruption, inflation, economic recession, and descrimination. The rampant dissatisfaction among civilians escalated and finally ignited the riot of “February 28th” (228) in 1947.

This violence resulted in tens of thousands of deaths. However, the tragedies didn’t end there. In 1949, the government went on to enforce martial law lasting for 38 years during which many people were accused as political dissidents and disappeared by the “White Terror”.

It wasn’t until 1987 that the martial law was lifted. Taiwan underwent various clashes and upheavals to establish a regime, which eventually shaped the vibrant and thriving democracy we have today.
﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏
▞ 228事件、白色恐怖，如何影響了現在的臺灣 ▚
﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋
228事件以及後來的白色恐怖，
在後來的時代裡，一直是台灣人共同承受的創傷記憶。
　
每年的2/28是228和平紀念日，
在這一天臺灣人會停班停課，
為的是提醒人們，反覆省思這個國家
在民主化道路上所經歷的一場災難。

- The effect of “the 228 incident” and the White Terror on Today’s Taiwan.
The wounds of “the 228 incident” and the White Terror are engraved into the hearts of the people. In memory of the “228 incident”, February 28th is marked as Peace Memorial Day, an official national holiday.

﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏
▞ 寫在228，酒保 Irene 想說的是 ▚
﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋
「一個人走得快，但一群人走得久」
走過極權體制，讓臺灣更懂得珍惜民主。
臺灣人不只要讓臺灣走得久，還會讓臺灣走得更好。

“Alone we can do so little, together we can do so much. “

After experiencing totalitarianism, the Taiwanese cherish the value of democracy. Together with combined forces, we’ll make Taiwan a better and brighter place.

6/20 世界難民の日にオンライン配信された100万人のキャンドルナイトｘUNHCR Will2Live2021に出演した時の模様をお届け！


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----- What's MIYAVI -----
アーティスト / ギタリスト
エレクトリックギターをピックを使わずに全て指で弾くという独自の“スラップ奏法”でギタリストとして世界中から注目を集め、これまでに約30カ国350公演以上のライブと共に、8度のワールドツアーを成功させている。
昨年7月には3年ぶりのオリジナルアルバム『NO SLEEP TILL TOKYO』を全世界で発売。発売日にはドジャースタジアムで行われた大リーグ始球式での国歌演奏で観客を魅了し、日本、アメリカにて話題騒然となった。
アンジェリーナ・ジョリー監督映画「Unbroken」（2016年日本公開）では俳優としてハリウッドデビューも果たした他、国内では「BLEACH」「ギャングース」、国外では「コングー髑髏島の巨神」「マレフィセント２」（2019年10月日米同時公開）への出演、モデルとして、Yohji Yamamoto, Y-3、最近では、Moncler BEYOND ワールドワイドキャンペーンに抜擢されるなど、各方面でも注目を集めている。
映画『Mission: Impossible ‒Rogue Nation』日本版テーマソングのアレンジ制作、HONDA コマーシャル楽曲、SMAPへの楽曲提供をはじめ様々なアーティスト作品へ参加するなど、国内外のアーティスト/クリエイターから高い評価を受けている。2017年にはUNHCR大使に就任。
常に世界に向けて挑戦を続ける“サムライ・ギタリスト”であり、ワールドワイドに活躍する今後最も期待のおける日本人アーティストの一人である。


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https://www.hulu.jp/the-first-bmsg-au...

-BMSG BOYS GROUP AUDITION 2021 特設サイト-
https://bmsg.tokyo/thefirst/

■ SNS
- Twitter
https://twitter.com/SkyHidaka

- Staff Twitter
https://twitter.com/SKYHI_STAFF

- Instagram
https://www.instagram.com/skyhidaka/

----- Information -----
企画・制作：ALPHABOAT
https://www.alpha-boat.com/

制作協力：WONDER&CLOCKS/ワンクロ
https://www.wonder-clocks.com/

お仕事のお問い合わせ
ab-pr@alpha-boat.com

目薬などの使用なし！約5分間の一本勝負！マジ泣きシーンをノーカットでアップします！

ボーイズグループオーディション「THE FIRST」テーマソング”To The First” 配信中！ https://SKY-HI.lnk.to/tothefirst

#SKYHI #THEFIRST

-リリース情報-
DIGITAL SINGLE「To The First」
配信LINK
https://SKY-HI.lnk.to/tothefirst


-YouTube-
[BMSG Audition 2021 -THE FIRST-] #1-1
https://youtu.be/dLidZx0bpc4

[BMSG Audition 2021 -THE FIRST-] #1-2
https://youtu.be/Q84wGOSvNhQ

To The First (Prod. Ryosuke “Dr.R” Sakai) -Music Video-
https://youtu.be/Mlh9zO0GBP0


-番組情報-
日本テレビ系「スッキリ」
毎週月～金曜 08:00～10:25
https://www.ntv.co.jp/sukkiri/

Hulu「THE FIRST -BMSG Audition 2021-」
毎週金曜20:00に新エピソード追加
https://www.hulu.jp/the-first-bmsg-au...

-BMSG BOYS GROUP AUDITION 2021 特設サイト-
https://bmsg.tokyo/thefirst/


■ SNS
- Twitter
https://twitter.com/SkyHidaka

- Staff Twitter
https://twitter.com/SKYHI_STAFF

- Instagram
https://www.instagram.com/skyhidaka/

----- Information -----
企画・制作：ALPHABOAT
https://www.alpha-boat.com/

制作協力：WONDER&CLOCKS/ワンクロ
https://www.wonder-clocks.com/

お仕事のお問い合わせ
ab-pr@alpha-boat.com