Ordinal theory is is a protocol for assigning serial numbers to satoshis, the smallest subdivision of a bitcoin, and tracking those satoshis as they are spent by transactions.
These serial numbers are large numbers, like this 804766073970493. Every satoshi, which is ¹⁄₁₀₀₀₀₀₀₀₀ of a bitcoin, has an ordinal number.
Nope! Ordinal theory works right now, without a side chain, and the only token needed is bitcoin itself.
Collecting, trading, and scheming. Ordinal theory assigns identities to individual satoshis, allowing them to be individually tracked and traded, as curios and for numismatic value.
Ordinal theory also enables inscriptions, a protocol for attaching arbitrary content to individual satoshis, turning them into bitcoin-native digital artifacts.
Ordinal numbers are assigned to satoshis in the order in which they are mined. The first satoshi in the first block has ordinal number 0, the second has ordinal number 1, and the last satoshi of the first block has ordinal number 4,999,999,999.
Satoshis live in outputs, but transactions destroy outputs and create new ones, so ordinal theory uses an algorithm to determine how satoshis hop from the inputs of a transaction to its outputs.
Fortunately, that algorithm is very simple.
Satoshis transfer in first-in-first-out order. Think of the inputs to a transaction as being a list of satoshis, and the outputs as a list of slots, waiting to receive a satoshi. To assign input satoshis to slots, go through each satoshi in the inputs in order, and assign each to the first available slot in the outputs.
Let's imagine a transaction with three inputs and two outputs. The inputs are on the left of the arrow and the outputs are on the right, all labeled with their values:
   →  
Now let's label the same transaction with the ordinal numbers of the satoshis that each input contains, and question marks for each output slot. Ordinal numbers are large, so let's use letters to represent them:
[a b] [c] [d e f] → [? ? ? ?] [? ?]
To figure out which satoshi goes to which output, go through the input satoshis in order and assign each to a question mark:
[a b] [c] [d e f] → [a b c d] [e f]
What about fees, you might ask? Good question! Let's imagine the same transaction, this time with a two satoshi fee. Transactions with fees send more satoshis in the inputs than are received by the outputs, so to make our transaction into one that pays fees, we'll remove the second output:
   → 
The satoshis e and f now have nowhere to go in the outputs:
[a b] [c] [d e f] → [a b c d]
So they go to the miner who mined the block as fees. The BIP has the details, but in short, fees paid by transactions are treated as extra inputs to the coinbase transaction, and are ordered how their corresponding transactions are ordered in the block. The coinbase transaction of the block might look like this:
[SUBSIDY] [e f] → [SUBSIDY e f]
An inscription is an NFT, but the term "digital artifact" is used instead, because it's simple, suggestive, and familiar.
The phrase "digital artifact" is highly suggestive, even to someone who has never heard the term before. In comparison, NFT is an acronym, and doesn't provide any indication of what it means if you haven't heard the term before.
Additionally, "NFT" feels like financial terminology, and the both word "fungible" and sense of the word "token" as used in "NFT" is uncommon outside of financial contexts.
Inscriptions are always immutable.
There is simply no way to for the creator of an inscription, or the owner of an inscription, to modify it after it has been created.
Ethereum NFTs can be immutable, but many are not, and can be changed or deleted by the NFT contract owner.
In order to make sure that a particular Ethereum NFT is immutable, the contract code must be audited, which requires detailed knowledge of the EVM and Solidity semantics.
It is very hard for a non-technical user to determine whether or not a given Ethereum NFT is mutable or immutable, and Ethereum NFT platforms make no effort to distinguish whether an NFT is mutable or immutable, and whether the contract source code is available and has been audited.
Inscription content is always on-chain.
There is no way for an inscription to refer to off-chain content. This makes inscriptions more durable, because content cannot be lost, and scarcer, because inscription creators must pay fees proportional to the size of the content.
Some Ethereum NFT content is on-chain, but much is off-chain, and is stored on platforms like IPFS or Arweave, or on traditional, fully centralized web servers. Content on IPFS is not guaranteed to continue to be available, and some NFT content stored on IPFS has already been lost. Platforms like Arweave rely on weak economic assumptions, and will likely fail catastrophically when these economic assumptions are no longer met. Centralized web servers may disappear at any time.
It is very hard for a non-technical user to determine where the content of a given Ethereum NFT is stored.
Inscriptions are much simpler.
Ethereum NFTs depend on the Ethereum network and virtual machine, which are highly complex, constantly changing, and which introduce changes via backwards-incompatible hard forks.
Inscriptions, on the other hand, depend on the Bitcoin blockchain, which is relatively simple and conservative, and which introduces changes via backwards-compatible soft forks.
Inscriptions are more secure.
Inscriptions inherit Bitcoin's transaction model, which allow a user to see exactly which inscriptions are being transferred by a transaction before they sign it. Inscriptions can be offered for sale using partially signed transactions, which don't require allowing a third party, such as an exchange or marketplace, to transfer them on the user's behalf.
By comparison, Ethereum NFTs are plagued with end-user security vulnerabilities. It is commonplace to blind-sign transactions, grant third-party apps unlimited permissions over a user's NFTs, and interact with complex and unpredictable smart contracts. This creates a minefield of hazards for Ethereum NFT users which are simply not a concern for ordinal theorists.
Inscriptions are scarcer.
Inscriptions require bitcoin to mint, transfer, and store. This seems like a downside on the surface, but the raison d'etre of digital artifacts is to be scarce and thus valuable.
Ethereum NFTs, on the other hand, can be minted in virtually unlimited qualities with a single transaction, making them inherently less scarce, and thus, potentially less valuable.
Inscriptions do not pretend to support on-chain royalties.
On-chain royalties are a good idea in theory but not in practice. Royalty payment cannot be enforced on-chain without complex and invasive restrictions. The Ethereum NFT ecosystem is currently grappling with confusion around royalties, and is collectively coming to grips with the reality that on-chain royalties, which were messaged to artists as an advantage of NFTs, are not possible, while platforms race to the bottom and remove royalty support.
Inscriptions avoid this situation entirely by making no false promises of supporting royalties on-chain, thus avoiding the confusion, chaos, and negativity of the Ethereum NFT situation.
Inscriptions unlock new markets.
Bitcoin's market capitalization and liquidity are greater than Ethereum's by a large margin. Much of this liquidity is not available to Ethereum NFTs, since many Bitcoiners prefer not to interact with the Ethereum ecosystem due to concerns related to simplicity, security, and decentralization.
Such Bitcoiners may be more interested in inscriptions than Ethereum NFTs, unlocking new classes of collector.
Inscriptions have a richer data model.
Inscriptions consist of a content type, also known as a MIME type, and content, which is an arbitrary byte string. This is the same data model used by the web, and allows inscription content to evolve with the web, and come to support any kind of content supported by web browsers, without requiring changes to the underlying protocol.
RGB and Taro are both second-layer asset protocols built on Bitcoin. Compared to inscriptions, they are much more complicated, but much more featureful.
Ordinal theory has been designed from the ground up for digital artifacts, whereas the primary use-case of RGB and Taro are fungible tokens, so the user experience for inscriptions is likely to be simpler and more polished than the user experience for RGB and Taro NFTs.
RGB and Taro both store content off-chain, which requires additional infrastructure, and which may be lost. By contrast, inscription content is stored on-chain, and cannot be lost.
Ordinal theory, RGB, and Taro are all very early, so this is speculation, but ordinal theory's focus may give it the edge in terms of features for digital artifacts, including a better content model, and features like globally unique symbols.
Counterparty has its own token, XCP, which is required for some functionality, which makes most bitcoiners regard it as an altcoin, and not an extension or second layer for bitcoin.
Ordinal theory has been designed from the ground up for digital artifacts, whereas Counterparty was primarily designed for financial token issuance.
Inscriptions are on Bitcoin. Bitcoin is the digital currency with the highest status and greatest chance of long-term survival. If you want to guarantee that your art survives into the future, there is no better way to publish it than as inscriptions.
Cheaper on-chain storage. At $20,000 per BTC and the minimum relay fee of 1 satoshi per vbyte, publishing inscription content costs $50 per 1 million bytes.
Inscriptions are early! Inscriptions are still in development, and have not yet launched on mainnet. This gives you an opportunity to be an early adopter, and explore the medium as it evolves.
Inscriptions are simple. Inscriptions do not require writing or understanding smart contracts.
Inscriptions unlock new liquidity. Inscriptions are more accessible and appealing to bitcoin holders, unlocking an entirely new class of collector.
Inscriptions are designed for digital artifacts. Inscriptions are designed from the ground up to support NFTs, and feature a better data model, and features like globally unique symbols and enhanced provenance.
Inscriptions do not support on-chain royalties. This is negative, but only depending on how you look at it. On-chain royalties have been a boon for creators, but have also created a huge amount of confusion in the Ethereum NFT ecosystem. The ecosystem now grapples with this issue, and is is engaged in a race to the bottom, towards a royalties-optional future. Inscriptions have no support for on-chain royalties, because they are technically infeasible. If you choose to create inscriptions, there are many ways you can work around this limitation: withhold a portion of your inscriptions for future sale, to benefit from future appreciation, or perhaps offer perks for users who respect optional royalties.
Inscriptions are simple, clear, and have no surprises. They are always immutable and on-chain, with no special due diligence required.
Inscriptions are on Bitcoin. You can verify the location and properties of inscriptions easily with Bitcoin full node that you control.
Let me begin this section by saying: the most important thing that the Bitcoin network does is decentralize money. All other use-cases are secondary, including ordinal theory. The developers of ordinal theory understand and acknowledge this, and believe that ordinal theory helps, at least in a small way, Bitcoin's primary mission.
Unlike many other things in the altcoin space, digital artifacts have merit. There are, of course, a great deal of NFTs that are ugly, stupid, and fraudulent. However, there are many that are fantastically creative, and creating and collecting art has been a part of the human story since its inception, and predates even trade and money, which are also ancient technologies.
Bitcoin provides an amazing platform for creating and collecting digital artifacts in a secure, decentralized way, that protects users and artists in the same way that it provides an amazing platform for sending and receiving value, and for all the same reasons.
Ordinals and inscriptions increase demand for Bitcoin block space, which increase Bitcoin's security budget, which is vital for safeguarding Bitcoin's transition to a fee-dependent security model, as the block subsidy is halved into insignificance.
Inscription content is stored on-chain, and thus the demand for block space for use in inscriptions is unlimited. This creates a buyer of last resort for all Bitcoin block space. This will help support a robust fee market, which ensures that Bitcoin remains secure.
Inscriptions also counter the narrative that Bitcoin cannot be extended or used for new use-cases. If you follow projects like DLCs, Fedimint, Lightning, Taro, and RGB, you know that this narrative is false, but inscriptions provide a counter argument which is easy to understand, and which targets a popular and proven use case, NFTs, which makes it highly legible.
If inscriptions prove, as the authors hope, to be highly sought after digital artifacts with a rich history, they will serve as a powerful hook for Bitcoin adoption: come for the fun, rich art, stay for the decentralized digital money.
Inscriptions are an extremely benign source of demand for block space. Unlike, for example, stablecoins, which potentially give large stablecoin issuers influence over the future of Bitcoin development, or DeFi, which might centralize mining by introducing opportunities for MEV, digital art and collectables on Bitcoin, are unlikely to produce individual entities with enough power to corrupt Bitcoin. Art is decentralized.
Inscription users and service providers are incentivized to run Bitcoin full nodes, to publish and track inscriptions, and thus throw their economic weight behind the honest chain.
Ordinal theory and inscriptions do not meaningfully affect Bitcoin's fungibility. Bitcoin users can ignore both and be unaffected.
We hope that ordinal theory strengthens and enriches bitcoin, and gives it another dimension of appeal and functionality, enabling it more effectively serve its primary use case as humanity's decentralized store of value.