Recursive Inscription: The Cornerstone of BTC Lego Combinations and Complex Logic Products

Original Title: recursive inscription the cornerstone of btc lego and complex logical products

Written by: @JellyZhouishere, @GryphsisAcademy

TL ; DR

• Recursive inscriptions, as a recent major update to Ordinals, open up vast imaginative possibilities for the composability development of the Ordinals protocol.
• Recursive inscriptions are a standard for inscription parsing, allowing PFP collection inscriptions to be created by uploading corresponding element features, enabling combinations without the need to upload or download actual images. Recursive inscriptions feature enhanced interoperability, reduced costs, and the ability to break through the 4MB limit on inscription size.
• Creative directions based on recursive inscriptions include: inscription disassembly and combination, Bitcoin music, Bitcoin chain games, generative art, decentralized websites, etc. This article details some typical cases that combine recursive inscriptions, showcasing their powerful potential.
• Recursive inscriptions also face some challenges: whether off-chain rendering parsers can quickly parse as the recursive levels increase; whether off-chain rendering parsers can quickly parse as the number of referenced inscriptions increases, etc. Theoretically, games or NFTs generated by recursive inscriptions can be infinitely complex and detailed. However, due to the limitations of the BTC network itself, indirect technical solutions are needed for implementation.
• Recursive inscriptions allow inscriptions to interact with each other, enabling new use cases. Generative art, on-chain displays, and efficient storage have become a reality. We can look forward to the deep adoption of recursive inscriptions in generative art, chain games, metaverse, and other fields, believing that future killer applications are in the making.

I. Introduction

The birth of the Ordinals protocol provides Bitcoin with the functionality of numbering and inscriptions, thereby broadening the range of products in the Bitcoin ecosystem and bringing immense application potential to the Bitcoin ecosystem.

In just the past few months, we have seen the Ordinals track grow from obscurity to a full-fledged ecosystem, during which the Ordinals protocol has also undergone significant upgrades and produced a series of derivative protocols:

In our June series of articles on Ordinals, we also updated detailed introductions to various derivative protocols of Ordinals and BRC20 (link: https://medium.com/@gryphsisacademy/diving-into-ordinals-how-to-bet-on-bitcoin-ecosystem-as-halving-approaches-3486db8cbf12), among which the recent major update of Ordinals—the emergence of recursive inscriptions—cannot be overlooked.

Recursive inscriptions were announced on June 12 by Raph, the new chief maintainer of the Bitcoin protocol Ordinals, who further merged the recursive inscription update 2167 proposed by Ordinals creator Casey Rodarmor into the Ordinals code, thereby opening up vast imaginative possibilities for the composability development of the Ordinals protocol.

This article will explore the principles of recursive inscriptions and their impact on Ordinals, and further look ahead to potential innovative application directions of recursive inscriptions based on existing cases.

II. Basic Principles and Technology of the Ordinals Protocol

Since the end of December 2022, Casey Rodarmor released the Ordinals protocol, introducing NFTs to the Bitcoin network through Ordinals and Inscriptions. This protocol allows any content, such as text, images, videos, or even applications, to be added to sequentially numbered sats (the smallest unit of Bitcoin) to create unique digital artifacts that can be transmitted over the Bitcoin network. Below, we outline the important technical principles involved in the Ordinals protocol:

(1) UTXO

Bitcoin employs a payment model known as "Unspent Transaction Output" (UTXO), where all balances are stored in a list of UTXOs. Each UTXO contains a certain amount of Bitcoin, owner information, and indicates whether it is available.

In a Bitcoin transaction, each transaction has inputs and outputs. Inputs reference existing UTXOs, while outputs specify new addresses and amounts. Once a transaction is initiated, the inputs lock the relevant UTXOs to prevent double spending until the transaction is confirmed. After confirmation, the input UTXOs are removed, and new UTXOs are generated from the outputs.

The total input amount of a transaction usually exceeds the total output, with the difference referred to as the network fee, which rewards miners for packaging transactions. Network fees are proportional to transaction complexity, and multi-input-output transactions typically incur higher fees.

(2) Satoshi Numbering and Tracking

There are a total of 21 million * 10^8 satoshis on the Bitcoin network. How does the Ordinals protocol uniquely number each satoshi and track its associated account?

According to the Ordinals protocol, the numbering of satoshis is determined by the order in which they are mined. The metadata of Ordinals is not stored in a specific location but is embedded in the witness data of transactions, which is "inscribed" in specific parts of Bitcoin transactions, and this data is attached to specific satoshis.

This process is achieved through Segregated Witness (SegWit) and "Pay-to-Taproot" (P2TR), allowing any form of content (such as text, images, or videos) to be inscribed on designated satoshis.

(3) SegWit and Taproot Upgrades

SegWit is an important protocol upgrade for Bitcoin that separates some transaction signature data (witness data) from the transaction itself, thereby reducing the size of data stored in Bitcoin blocks. This initiative expands the capacity of blocks, allowing them to accommodate more transactions, improving the network's transaction processing capability, and lowering transaction fees.

The SegWit protocol upgrade introduced a new witness field in transaction outputs to enhance privacy and performance. Although the original design of witness data was not intended for data storage, it actually provides us with the opportunity to store metadata such as inscriptions.

The Taproot protocol upgrade introduced in 2021 allows different transaction conditions to be stored more privately on the blockchain. Through Taproot script paths, we can store inscription content in spending scripts, which have almost no limitations in terms of content. Moreover, due to Taproot's discount mechanism, storing inscription content becomes more economical, saving a significant amount of resources.

The Ordinals protocol cleverly utilizes SegWit to relax the limits on the size of content written to the Bitcoin network, allowing inscription content to be stored in witness data, with a maximum capacity of 4MB of metadata. Taproot makes it easier to store any witness data in Bitcoin transactions, enabling Ordinals developer Casey Rodarmor to reuse old opcodes (OPFALSE, OPIF, OP_PUSH) to describe content encapsulated as inscriptions, thereby storing arbitrary data.

(4) The Process of Minting Inscriptions

• Commit: The first step is to create an output that points to a Taproot script containing the inscription content in the commit transaction. This output uses the Taproot storage format. At this point, the inscription data is associated with the UTXO of the transaction output but is not yet public.
• Reveal: At this stage, a transaction is initiated using the UTXO corresponding to the inscription as input. At this point, the corresponding inscription content is revealed to the entire network.

Through these two steps, the inscription content is now bound to its inscribed UTXO. Next, based on the previously mentioned satoshis, the inscription is realized on the first satoshi corresponding to the input UTXO. The inscription content is included in the input that displays the transaction. This specially inscribed satoshi can be transferred, purchased, sold, lost, and recovered.

III. Principles and Implementation of Bitcoin Recursive Inscriptions

Having understood the basic principles of Ordinals, let's look at recursive inscriptions:

The Ordinals protocol introduces the ability to fully inscribe files on-chain in Bitcoin. Before the emergence of recursive inscriptions, inscriptions were like isolated and limited islands. While you could inscribe text, images, and code, they could not interact with each other.

However, with the introduction of recursive inscriptions, the situation is about to change. Now, inscriptions can use the special "/-/content/:inscription_id" syntax to request the content of other inscriptions. This allows users to create inscriptions on the Bitcoin chain using less capacity and lower fees.

Recursive inscriptions are a standard for inscription parsing. Their syntax is essentially similar to using code to find images, allowing PFP collection inscriptions to be created by uploading the corresponding patterns, colors, actions, and other element features, and then combining existing corresponding elements on-chain without the need to upload or download actual images.

Recursive inscriptions have the following characteristics:

• Through the unique self-referential property of recursive inscriptions, we have the opportunity to break the constraints of previous inscription methods, escaping the awkward state of each inscription being isolated and unrelated, thus opening up the possibility of creating freely combinable elements.
• Recursive inscriptions maintain a small size in their textual code form, not only reducing costs but also allowing the size of inscriptions to break through the 4MB limit of Bitcoin blocks.
• This advancement enhances interoperability, programmability, and scalability, injecting more possibilities and creative imagination into the Bitcoin chain.
• From a protocol perspective, the future prospects are very broad, with rich narratives waiting for developers and users to construct and utilize.

However, there are still some challenges, such as whether inscriptions can be indexed and launched on platforms, which will determine the speed of their development and the extent of their widespread recognition.

IV. Innovative Application Methods of Bitcoin Recursive Inscriptions

The emergence of recursive inscriptions unlocks many powerful innovative applications. With high flexibility, combinability, and low-cost advantages, recursive inscriptions bring infinite new possibilities. Below, this article will introduce some specific cases to illustrate the potential innovations and application directions of recursive inscriptions.

Through recursion, inscriptions can easily reference the code of other inscriptions. The content of one inscription can now be used by many other inscriptions. This new composability opens up possibilities in areas we have hardly explored, such as inscribing complex images, videos, 3D games, and more on-chain. Recursive inscriptions make the establishment of an internal internet possible. More possibilities include secondary creation of inscriptions, decentralized GitHub, NFT combination fragmentation, and so on. Utilizing recursive inscriptions, we can achieve the following creative ideas:

Below, we will detail some typical cases that showcase the powerful potential of recursive inscriptions:

(1) On-chain Generative Art: 1Mask

By further combining various initial schemes mentioned earlier, various collections can be created, and secondary creations of inscriptions can be achieved: for example, combining a1 and a2 within collection a, or combining collection a and collection b. On this basis, a truly community-driven native interactive generative art is expected to emerge on the BTC chain.

Let's look at the first case: 1Mask.

This is a mask-themed fully on-chain generative art project on the BTC chain. The 1Mask project cleverly integrates the recursive technology of Ordinals, consisting of three intertwined elements: templates, algorithms, and inscription generation.

Source: https://1mask.io/

The template part contains seven inscriptions, each corresponding to a unique type of template, with a format following image/svg + xml.

The basic principle of the algorithm is to use the user's wallet address as a seed, employing random functions to create various color combinations for coloring the mask model.

The inscription generation mechanism utilizes recursive technology to reference algorithm inscriptions. Each mask inscription embeds the HTML code necessary to construct the final colorful mask image. This is achieved by executing the code embedded in the algorithm inscription using a random seed filled with user-specific on-chain data (such as wallet address), making it random yet relevant to the user. Therefore, the same wallet address will always produce consistent results when using the same template.

Whenever a brand new mask inscription is created, it incorporates user-specific on-chain details and references the algorithm inscription. With the power of recursive inscription technology, once the newly created mask inscription enters the market or is indexed by a wallet, it autonomously activates the reference code contained in the algorithm inscription. When these codes run, they use user-specific on-chain data as input, ultimately displaying a unique and personalized mask image.

In the Bitcoin network environment, the data contained in inscriptions is immutable, ensuring its integrity. This characteristic determines that the real-time images presented based on this unchangeable inscription data are also immutable. As long as the random seed and algorithm involved in the mask inscription are correct, users can verify the authenticity and accuracy of the creative process at any time.

Behind this project, 1Mask further introduced a standard called BRC721Auto, proposing that fully on-chain generative art consists of at least two types of inscriptions: one is the code inscription, and the other is the personalized parameter inscription.

In the code inscription, we need to encode an algorithm that can automatically generate HTML DOM based on the content of the parameters. This DOM can be a canvas, SVG, or other content that can be recognized and rendered as graphics by the browser.

Of course, the code inscription can also reference the content of other inscriptions to complete its algorithm.

In the parameter inscription, we need to define an HTML and specify a global parameter p to reference a Code Inscription. When a regular browser attempts to display this Parameter Inscription, it will recognize the global parameter p and automatically execute the start() function in the Code Inscription to add or modify the current HTML's DOM, ultimately rendering the content of this HTML. Therefore, the parameter inscription can be seen as the final NFT (Non-Fungible Token).

With the Recursive Inscription technology, the code required to generate graphics, the execution process of the code, and the verification process are all protected under the consensus of the Bitcoin blockchain. Unless someone can launch a 51% attack on Bitcoin, no one can control the generation process of ERC721 Auto NFTs, which will be autonomously executed by the Bitcoin ecosystem.

1Mask also further proposed three major standards for fully on-chain generative art projects. These three standards are:

• Decentralized storage of automatically generated graphic code
• Decentralized execution of code based on user-provided parameters for personalized graphic generation
• Decentralized verification of the correctness of the generated results

Based on these standards, it is not difficult to see that on-chain art based on recursive inscriptions has the following characteristics:

• Uniqueness and randomness: The work must be generated through algorithms and smart contracts, possessing irreplaceability and uniqueness, provably random on-chain revelations, and also needs to have certain artistic and aesthetic value.
• Interactivity: Users can interact with and control the work.
• Decentralization: The art is fully on-chain, completely decentralized in storage, and no centralized institution or individual can control it.
• Reusable code, and it is based on Ordinals' works.

Compared to generative art projects on other chains like Ethereum, generative art based on BTC recursive inscriptions is fully on-chain generative art, independent, and decentralized generative art that does not rely on any off-chain resources.

(2) Geek Project: Orbinals

Due to the flexibility of recursive inscriptions, it provides a stage for geeks to showcase their talents, with projects rich in geek spirit further exploring the various possibilities of Ordinals technology.

"Orbinals" is a typical representative of this, a geek project without Twitter or a website, with all project content based on Uncommon sat, showing that as of August 20, the price of Uncommon sat has reached over $366.

Source: https://www.ord.io/?satributes=uncommon&contentType=html&sortBy=newest

If you directly open the collection series website of Orbinals, you will find that each image in its celestial motion series references some of the same content, with some parameters differing. After digging into the referenced content in its recursive inscriptions, we can discover the true secrets of the project hidden in this reference link (https://ordin-delta.vercel.app/content/b5091b76f78d73677ad6b81e4785b0dfebc62b1079a0bf78b8366859a1ffacbci0, where Orbinals stands for "Orbinals: Three Body Orbit Artifacts on Ordinals," and behind it is programming the motion of three objects using HTML and JavaScript, based on two-body simulation code.

Source: https://evgenii.com/blog/three-body-problem-simulator/

Supported by mathematical and physical equations, the beauty of celestial motion is presented in a concise manner on the Bitcoin chain.

Moreover, since there are no Twitter, Discord, or official websites, the project is likely to use a very geeky approach, with future information presented on sats controlled by the team.

Source: https://ordin-delta.vercel.app/content/b5091b76f78d73677ad6b81e4785b0dfebc62b1079a0bf78b8366859a1ffacbci0

In addition to the four channels disclosed by the project team, there is also a hidden Easter egg: in the content of the inscriptions referenced by the project (https://ordin-delta.vercel.app/content/4f59fc257a7c78d4074dcd7a4a55360d56986f474700adc7dc37ac231901fc40i0, a string of instructions is hidden in the code: futureCommunicationchannelson/sats/acknowledge, and acknowledge happens to belong to a sats controlled by the team.

Source: https://www.ord.io/sat/1940129935364125

(3) BRC69 Project: Orditroops

BRC69 is a new standard for creating recursive collections released by Luminex (https://github.com/luminexord/brc69), which utilizes recursive inscriptions to optimize the cost of inscribing using the ordinal protocol on Bitcoin, facilitating the launch of recursive collections on Bitcoin. Additionally, BRC69 offers high flexibility and opens the door to more enhanced features and functionalities, paving the way for more interesting on-chain functionalities, such as preview features.

With BRC69, the cost of inscriptions for Ordinals collections can be reduced by over 90%. This reduction is achieved through a four-step process:

• Record features
• Deploy collections
• Compile collections
• Create assets

As long as the collection creator publishes the official inscription list of their collection according to current requirements, all these processes can be carried out without the need for external indexers. Moreover, images will automatically render on all front-end interfaces that have implemented recursive inscriptions without additional steps.

Orditroops is a recursive NFT based on BRC69, implementing the content of the BRC69 protocol, increasing the combinability of features, reducing the space occupied by images, and the flexible combinations of soldiers, weapons, and outfits add many characteristics and fun to this NFT collection.

Source: https://twitter.com/OrdiTroops

(4) 3D NFT Project: OCM (On-Chain Monkeys)

Source: https://www.ord.io/3563188a3db53850bba48747293def7bd6b7395e4241b29ec7d49892945cf927i0

OCM is the first 3D NFT project to apply the recursive inscription standard. OnChainMonkey was originally an NFT project created on Ethereum in September 2021, and earlier this year, the OnChainMonkey series appeared as the first 10k series inscribed on Bitcoin.

As a high-resolution 3D animated inscription, OCM quickly stands out for its detail and quality. It is worth noting that before it, most inscriptions were still small text files or low-resolution images. Even on 4K or 8K displays, OCM can provide better clarity, a quality achieved through files not exceeding 1 KB each, which previous projects found difficult to achieve.

OCM is able to achieve this because it was the first to use powerful recursive inscriptions. The first 300 inscriptions on Bitcoin were inscribed on 300 consecutive satoshis, starting from block 78 in 2009, sorted on-chain in ascending order of their satoshi numbers. The builders of OCM used compressed code and referenced the P5.js and Three.js libraries for future creators to use. Users can view and access the library in their browsers, automatically decompressing when rendering Dimensions Interactive Art in the Ordinals protocol.

Through recursive inscriptions, OCM efficiently utilizes block space (each less than 1 KB) and achieves random on-chain revelations, combining features such as high-definition quality, 3D, animation, and interactive art.

(5) On-chain Music Engine: Descent into Darkness Music Engine

Source: https://ordinals.com/content/6fd06768414dfc2bd68b55869eea6844864fbf71ee72ec26568520e313c2bda2i0

Input any word or phrase to generate unique on-chain music. This music engine is a companion product for the MUD RPG game "Descent Into Darkness," generating music through keyword input. Founder Ratoshi emphasized the important role of ChatGPT in developing the project’s music, and using recursive inscriptions helps significantly reduce costs. The special combination of blockchain technology and artificial intelligence pays homage to the classic music of retro video games.

(6) Single-player Chain Games

A game requires various components such as images, front-end, and business logic. If the total size of the materials is less than 4MB, it can be completed by inscribing a satoshi without the need for recursive inscriptions.

There are two scenarios where recursive inscription technology is suitable:

1. The material itself is large (greater than 4MB), for example, a background image of 5MB cannot be directly inscribed on a satoshi, but it can be split and placed in different satoshis for reference and display.
2. If better business logic is to be achieved, such as having 100 sat inscriptions as a series of games using the same JavaScript (JS) file, in this case, it is also suitable to use recursive inscriptions because there is no need to inscribe the JS file again for each sat.

The game's HTML (front-end) and JS (business logic) are inscribed on BTC's "satoshis," referencing each other to generate a single-player H5 mini-game.

Here are three examples of such single-player H5 mini-games:

a. Snake Game

Source: ord.io/431507

Bitcoin Snake Game, this game is a typical H5 single-player mini-game, also a well-known game: Snake. The front-end and execution logic of this game are all written on this satoshi, without using recursive inscription technology. The total number of NFTs in this series is 100. In fact, a better approach would be to inscribe the JS file (business logic) on one satoshi and then use 100 different inscribed HTML satoshis to reference (or recursively call) the satoshi where the JS file is located to generate the inscription. This would be much simpler.

b. Link Game

Source: ord.io/18201467

As shown in the image, this game is a 34 grid (this is the simple mode, while the complex mode is a 66 grid). You can click on two squares at a time, and if the images in the two squares are the same, they will be fixed; if not, they will display as a question mark. Completing the game within a limited number of clicks counts as a victory. Limiting the number of clicks tests the player's short-term memory. This game is similar to the well-known link game. The JS and HTML of this game are all inscribed on this satoshi, but it references the "background image" (as shown below), so it is a simple application of recursive inscriptions.

Source: ord.io/18201467

c. MUD Game

Source: https://ordinals.com/content/1915ae7d46502199a7d03256efd7f6e2f6aabb8ed7176b34f70b7b8fd778b36ci0

Descent into Darkness is a text-based role-playing game that combines classic MUD game elements with ordinals technology, providing players with a unique gaming experience.

In Descent into Darkness, players take on the role of an adventurer seeking a way out of the darkness, facing monsters, tasks, and boss battles. Players must fight monsters to complete tasks, unlock new missions, and earn coins to upgrade equipment and purchase items.

The above three single-player H5 mini-games are very simple applications. As games, they are incomplete; the processes of starting, progressing, and ending the game are not on-chain, and the game cannot be saved. After the game ends, the inscription of the satoshi does not change. It only defines the logic of the game without saving the game's state. This is merely a preliminary attempt at BTC chain games.

(7) Multi-player Full-chain Game: BTC PixelWar

Source: https://twitter.com/btcpixelwar

BTC PixelWar is a full-chain multi-player game on BTC, claiming to be the first full-chain multi-player game on the BTC chain. Participants create on a 256*256 pixel canvas. They can directly click on pixels or upload images to generate pixel points on the canvas. Each submission generates an inscription of the latest state of the entire canvas, with each generated inscription referencing the previously generated inscription state, creating a recursive chain of inscriptions. This may be the project with the most recursion currently on the market, and it is a landmark application in the field of recursive inscriptions.

The project proposes a new standard, "BRC721Cofound," which utilizes recursive inscriptions to allow all Bitcoin users to collaborate on the same canvas and record the process. Each moment is an inscription depicting the state of the collaboratively created canvas at that moment. This inscription is called a "moment inscription," containing newly added or updated pixels and referencing previous "moment inscriptions" along with the "code inscriptions" that handle the changes in images between the two moments. Considering that the number of participants in the painting may be large, rendering the latest canvas state requires deep recursion to load the pixels drawn by everyone. However, this process may lead to extended loading times. To address this issue, the "code inscription" is designed to take a snapshot of the latest canvas state after the current "moment inscription" rendering is completed. This snapshot is then stored in the DOM tree of the current "moment inscription." Therefore, sequential browsers can simplify the rendering process by caching the DOM tree of each rendered moment inscription, thereby reducing the levels of recursion.

Overall, BTC PixelWar is an innovative and landmark BTC multi-player full-chain game that achieves collaborative creation while optimizing the rendering process. The introduction of the "BRC721 Cofound" standard opens up new possibilities for multi-player game applications on the Bitcoin chain and demonstrates the potential of recursive inscriptions in gaming and social domains.

V. Challenges and Future Development of Bitcoin Recursive Inscriptions

Recursive inscriptions have opened the era of on-chain inscriptions 2.0, making the gameplay of BTC NFTs increasingly rich. The possibility of BTC NFTs diverging from those on Ethereum and other chains is becoming more likely, with vast imaginative/narrative space for the future.

Recursive inscriptions allow previously independent inscriptions to be directly connected and referenced, forming a structure of diverse databases. In previous articles, we discussed various derivative protocols based on Ordinals. In fact, combining recursive inscriptions with the aforementioned derivative protocols will enable them to read other inscriptions and respond based on their own intelligent instructions to update their states. Through indexing, they can directly manipulate the states of the protocols, forming a coherent set of actions similar to smart contracts.

At the same time, the vast recursive inscription database provides more operational and imaginative space for inscriptions, including foundational data, knowledge bases, code libraries, function libraries, and metadata from various fields, and they can directly reference each other to realize complex logical product applications. Therefore, we can look forward to the deep adoption of recursive inscriptions in generative art, chain games, metaverse, and other fields, believing that future killer applications are in the making.

At the same time, recursive inscriptions also face some challenges:

1. If the recursive levels increase, such as reaching ten thousand layers of recursion, whether off-chain rendering parsers can quickly parse.
2. If the number of referenced inscriptions increases, such as a satoshi referencing ten thousand inscriptions at the same time, whether off-chain rendering parsers can quickly parse.

If these two points can be achieved, theoretically, the games or NFTs generated by recursive inscriptions can be infinitely complex and detailed. These two issues are difficult to fundamentally resolve due to the limitations of the BTC network itself, but they can be implemented through indirect technical solutions.

VI. Conclusion

The recursive upgrade in the Ordinals protocol allows inscriptions to interact with each other, enabling new and exciting use cases. With this functionality, generative art, on-chain displays, and efficient storage have become a reality. We can see that developers within the BTC ecosystem are continuing to create and develop various projects in the fields of chain games and generative art. Works based on recursive inscriptions are emerging one after another, and various components of a large project are gradually coming together. In the future, we can further anticipate the birth of on-chain games, metaverse, interactive generative art, and other projects with complex product logic.

Reference:

https://github.com/1nftopia/brc721cofound

https://github.com/1nftopia/brc721auto/tree/main

https://medium.com/@gryphsisacademy/diving-into-ordinals-how-to-bet-on-bitcoin-ecosystem-as-halving-approaches-3486db8cbf12

Disclaimer: This report is an original work completed by students of @JellyZhouishere and @GryphsisAcademy, under the guidance of @979_eth and @Erjiueth. The author is solely responsible for all content, which does not necessarily reflect the views of Gryphsis Academy, nor does it necessarily reflect the views of the organization that commissioned the report. Editing content and decisions are not influenced by readers. Please be aware that the author may hold cryptocurrencies mentioned in this report. This document is for informational reference only and should not be used as the basis for investment decisions. It is strongly recommended that you conduct your own research and consult neutral financial, tax, or legal advisors before making investment decisions. Please remember that past performance of any asset does not guarantee future returns.