<pre>
  BIP: ?
  Layer: Applications
  Title: Ordinal Numbers
  Author: Casey Rodarmor <casey@rodarmor.com>
  Comments-Summary: No comments yet.
  Comments-URI: https://github.com/ordinals/ord/discussions/126
  Status: Draft
  Type: Informational
  Created: 2022-02-02
  License: PD
</pre>

== Introduction ==

=== Abstract ===

This document defines a scheme for assigning serial numbers to sats.

=== Copyright ===

This work is placed in the public domain.

=== Motivation ===

Bitcoin has no notion of stable, public accounts or identities. Addresses are
single-use, and wallet accounts are private. Additionally, the use of addresses
or public keys as stable identifiers precludes transfer of ownership or key
rotation.

This proposal is motivated by the desire to provide stable identifiers that may
be used by Bitcoin applications.

== Description ==

=== Design ===

Every sat is serially numbered, starting at 0, in the order in which it is
mined. These numbers are termed "ordinal numbers", or "ordinals", as they are
ordinal numbers in the mathematical sense, giving the order of each sat in the
total supply. The word "ordinal" is nicely unambiguous, as it is not used
elsewhere in the Bitcoin protocol.

The ordinal numbers of sats in transaction inputs are transferred to output
sats in first-in-first-out order, according to the size and order of the
transactions inputs and outputs.

If a transaction is mined with the same transaction ID as outputs currently in
the UTXO set, following the behavior of Bitcoin Core, the new transaction
outputs displace the older UTXO set entries, destroying the sats contained in
any unspent outputs of the first transaction. This rule is required to handle
the two pairs of mainnet transactions with duplicate transaction IDs, namely
the coinbase transactions of blocks 91812/91842, and 91722/91880, mined before
[https://github.com/bitcoin/bips/blob/master/bip-0034.mediawiki BIP-34] made
the creation of transactions with duplicate IDs impossible.

For the purposes of the assignment algorithm, the coinbase transaction is
considered to have an implicit input equal in size to the subsidy, followed by
an input for every fee-paying transaction in the block, in the order that those
transactions appear in the block. The implicit subsidy input carries the
block's newly created sats. The implicit fee inputs carry the sats that were
paid as fees in the block's transactions.

Underpaying the subsidy does not change the ordinal numbers of sats mined
in subsequent blocks. Ordinals depend only on how many sats could have been
mined, not how many actually were.

=== Specification ===

Sats are numbered and transferred with the following algorithm:

<pre>
# subsidy of block at given height
def subsidy(height):
  return 50 * 100_000_000 >> height // 210_000

# first ordinal of subsidy of block at given height
def first_ordinal(height):
  start = 0
  for height in range(height):
    start += subsidy(height)
  return start

# assign ordinals in given block
def assign_ordinals(block):
  first = first_ordinal(block.height)
  last = first + subsidy(block.height)
  coinbase_ordinals = list(range(first, last))

  for transaction in block.transactions[1:]:
    ordinals = []
    for input in transaction.inputs:
      ordinals.extend(input.ordinals)

    for output in transaction.outputs:
      output.ordinals = ordinals[:output.value]
      del ordinals[:output.value]

    coinbase_ordinals.extend(ordinals)

  for output in block.transaction[0].outputs:
    output.ordinals = coinbase_ordinals[:output.value]
    del coinbase_ordinals[:output.value]
</pre>

=== Terminology and Notation ===

A satpoint may be used to indicate the location of a sat within an output. A
satpoint consists of an outpoint, i.e., a transaction ID and output index, with
the addition of the offset of the ordinal within that output. For example, if
the sat in question is at offset 6 in the first output of a transaction, its
satpoint is:

`680df1e4d43016571e504b0b142ee43c5c0b83398a97bdcfd94ea6f287322d22:0:6`

== Discussion ==

=== Rationale ===

Ordinal numbers are designed to be orthogonal to other aspects of the Bitcoin
protocol, and can thus be used in conjunction with other layer one and layer
applications, even ones that were not designed with ordinal numbers in mind.

Ordinal sats can be secured using current and future script types. They can be
held by single-signature wallets, multi-signature wallets, time-locked, and
height-locked in all the usual ways.

By assigning ordinal numbers to all sats without the need for an explicit
creation step, the anonymity set of ordinal number users is maximized.

Since a sat has an output that contains it, and an output has a public key that
controls it, the owner of a sat can respond to challenges by signing messages
using the address associated with the controlling UTXO. Additionally, a sat can
change hands, or its private key can be rotated without a change of ownership,
by transferring it to a new output.

Ordinals require no changes to blocks, transactions, or network protocols, and
can thus be immediately adopted, or ignored, without impacting existing users.

Ordinals do not have an explicit on-chain footprint. However, a valid objection
is that adoption of ordinals will increase demand for outputs, and thus
increase the size of the UTXO set that full nodes must track. See the
objections section below.

The ordinal number scheme is extremely simple. The specification above is 15
lines of code.

Ordinals are fairly assigned. They are not premined, and are assigned
proportionally to existing bitcoin holders.

Ordinals are as granular as possible, as bitcoin is not capable of tracking
ownership of sub-sat values.

=== Transfer and the Dust Limit ===

Any single-sat transfer can be accomplished in a single transaction, but the
resulting transaction may contain outputs below the dust limit, and thus be
non-standard and difficult to get included in a block. Consider a scenario
where Alice owns an output containing the range of sats [0,10], the current
dust limit is 5 sats, and Alice wishes to send send sat 4 and 6 to Bob, but
retain ordinal 5. Alice could construct a transaction with three outputs of
size 5, 1, and 5, containing sats [0,4], 5, and [6,10], respectively. The
second output is under the dust limit, and so such a transaction would be
non-standard.

This transfer, and indeed any transfer, can be accomplished by breaking the
transfer into multiple transactions, with each transaction performing one or
more splits and merging in padding outputs as needed.

To wit, Alice could perform the desired transfer in two transactions. The first
transaction would send sats [0,4] to Bob, and return as change sat [5,10] to
Alice. The second transaction would take as inputs an output of at least 4
sats, the change input, and an additional input of at least one sat; and create
an output of size 5 to Bob's address, and the remainder as a change output.
Both transactions avoid creating any non-standard outputs, but still accomplish
the same desired transfer of sats.

=== Objections ===

''Privacy: Ordinal numbers are public and thus reduce user privacy.''

The applications using ordinal numbers required them to be public, and reduce
the privacy of only those users that decide to use them.

''Fungibility: Ordinal numbers reduce the fungibility of Bitcoin, as ordinals
received in a transaction may carry with them some public history.''

As anyone can send anyone else any sats, any reasonable person will assume that
a new owner of a particular sat cannot be understood to be the old owner, or
have any particular relationship with the old owner.

''Congestion: Adoption of ordinal numbers will increase the demand for
transactions, and drive up fees.''

Since Bitcoin requires the development of a robust fee market, this is a strong
positive of the proposal.

''UTXO set bloat: Adoption of ordinal numbers will increase the demand for
entries in the UTXO set, and thus increase the size of the UTXO set, which all
full nodes are required to track.''

The dust limit, which makes outputs with small values difficult to create,
should encourage users to create non-dust outputs, and to clean them up once
they no longer have use for the sats that they contain.

=== Security ===

The public key associated with a sat may change. This requires actively
following the blockchain to keep up with key changes, and requires care
compared to a system where public keys are static. However, a system with
static public keys suffers from an inability for keys to be rotated or accounts
to change hands.

Ordinal-aware software must avoid losing valuable sats by unintentionally
relinquishing them in a transaction, either to a non-controlled output or by
using them as fees.

=== Privacy considerations ===

Ordinals are opt-in, and should not impact the privacy of existing users.

Ordinals are themselves public, however, this is required by the fact that many
of the applications that they are intended to enable require public
identifiers.

Ordinal aware software should never mix sats which might have some publicly
visible data associated with their ordinals with sats intended for use in
payments or savings, since this would associate that publicly visible data with
the users otherwise pseudonymous wallet outputs.

=== Fungibility considerations ===

Since any sat can be sent to any address at any time, sats that are transferred,
even those with some public history, should be considered to be fungible with
other sats with no such history.

=== Backward compatibility ===

Ordinal numbers are fully backwards compatible and require no changes to the
bitcoin network.

=== Drawbacks ===

==== Large Index Size ====

Indexes supporting fast queries related to ordinals are slow to build and
consume large amounts of space.

An O(1) index that maps UTXOs to the ordinals that they contain is currently
100 GiB. The same index including spent outputs is 10 TiB.

An O(1) index supporting the opposite mapping, that of individual ordinals to
the UTXO that contains them, is likely to be intractable. However, an O(n)
index where n is the number of times an ordinal has changed hands, is fast and
practical.

==== Large Location Proofs ====

A proof can be constructed that demonstrates that a particular sat is contained
in a particular output, however the proofs are large. Such a proof consists of:

- Block headers
- A Merkle path to the coinbase transaction that created the sat
- The coinbase transaction that created the sat
- And for every spend of that sat:
  - The spend transaction
  - The transactions that created the inputs before the input that was spent,
    to determine the values of the preceding inputs, to determine the position
    of the sat
  - And, if the sat was used as fees, all prior transaction in the block in
    which it was spent, and the coinbase transaction, to determine the location
    of the sat in the outputs.

== Reference implementation ==

This document and an implementation of an index that tracks the position of
sats in the main chain are maintained [https://github.com/ordinals/ord here].

== References ==

A variation of this scheme was independently invented a decade ago by jl2012
[https://bitcointalk.org/index.php?topic=117224.0 on the Bitcoin Forum].

For other colored coin proposals see [https://en.bitcoin.it/wiki/Colored_Coins the
Bitcoin Wiki entry].

For aliases, an implementation of short on-chain identifiers, see
[https://github.com/bitcoin/bips/blob/master/bip-0015.mediawiki BIP 15].
