Ordinal Theory Overview

Ordinals are a numbering scheme for gros that allows tracking and transferring individual gros. These numbers are called ordinal numbers. Gros are numbered in the order in which they're mined, and transferred from transaction inputs to transaction outputs first-in-first-out. Both the numbering scheme and the transfer scheme rely on order, the numbering scheme on the order in which gros are mined, and the transfer scheme on the order of transaction inputs and outputs. Thus the name, ordinals.

Technical details are available in the BIP.

Ordinal theory does not require a separate token, another blockchain, or any changes to Groestlcoin. It works right now.

Ordinal numbers have a few different representations:

  • Integer notation: 2099994106992659 The ordinal number, assigned according to the order in which the gro was mined.

  • Decimal notation: 3891094.16797 The first number is the block height in which the gro was mined, the second the offset of the gro within the block.

  • Degree notation: 3°111094′214″16797‴. We'll get to that in a moment.

  • Percentile notation: 99.99971949060254% . The gro's position in Groestlcoin's supply, expressed as a percentage.

  • Name: satoshi. An encoding of the ordinal number using the characters a through z.

Arbitrary assets, such as NFTs, security tokens, accounts, or stablecoins can be attached to gros using ordinal numbers as stable identifiers.

Ordinals is an open-source project, developed on GitHub. The project consists of a BIP describing the ordinal scheme, an index that communicates with a Groestlcoin Core node to track the location of all gros, a wallet that allows making ordinal-aware transactions, a block explorer for interactive exploration of the blockchain, functionality for inscribing gros with digital artifacts, and this manual.

Rarity

Humans are collectors, and since gros can now be tracked and transferred, people will naturally want to collect them. Ordinal theorists can decide for themselves which gros are rare and desirable, but there are some hints…

Groestlcoin has periodic events, some frequent, some more uncommon, and these naturally lend themselves to a system of rarity. These periodic events are:

  • Blocks: A new block is mined approximately every 1 minute, from now until the end of time.

  • Difficulty adjustments: Every 2016 blocks, or approximately every 1.5 days, the Groestlcoin network responds to changes in hashrate by adjusting the difficulty target which blocks must meet in order to be accepted.

  • Halvings: Every 1,050,000 blocks.

  • Cycles: Every 6 * 1,050,000 blocks.

This gives us the following rarity levels:

  • common: Any gro that is not the first gro of its block
  • uncommon: The first gro of each block
  • rare: The first gro of each difficulty adjustment period
  • epic: The first gro of each halving epoch
  • legendary: The first gro of each cycle
  • mythic: The first gro of the genesis block

Which brings us to degree notation, which unambiguously represents an ordinal number in a way that makes the rarity of a gro easy to see at a glance:

A°B′C″D‴
│ │ │ ╰─ Index of gro in the block
│ │ ╰─── Index of block in difficulty adjustment period
│ ╰───── Index of block in halving epoch
╰─────── Cycle, numbered starting from 0

Ordinal theorists often use the terms "hour", "minute", "second", and "third" for A, B, C, and D, respectively.

Now for some examples. This gro is common:

1°1′1″1‴
│ │ │ ╰─ Not first gro in block
│ │ ╰─── Not first block in difficulty adjustment period
│ ╰───── Not first block in halving epoch
╰─────── Second cycle

This gro is uncommon:

1°1′1″0‴
│ │ │ ╰─ First gro in block
│ │ ╰─── Not first block in difficulty adjustment period
│ ╰───── Not first block in halving epoch
╰─────── Second cycle

This gro is rare:

1°1′0″0‴
│ │ │ ╰─ First gro in block
│ │ ╰─── First block in difficulty adjustment period
│ ╰───── Not the first block in halving epoch
╰─────── Second cycle

This gro is epic:

1°0′1″0‴
│ │ │ ╰─ First gro in block
│ │ ╰─── Not first block in difficulty adjustment period
│ ╰───── First block in halving epoch
╰─────── Second cycle

This gro is legendary:

1°0′0″0‴
│ │ │ ╰─ First gro in block
│ │ ╰─── First block in difficulty adjustment period
│ ╰───── First block in halving epoch
╰─────── Second cycle

And this gro is mythic:

0°0′0″0‴
│ │ │ ╰─ First gro in block
│ │ ╰─── First block in difficulty adjustment period
│ ╰───── First block in halving epoch
╰─────── First cycle

If the block offset is zero, it may be omitted. This is the uncommon gro from above:

1°1′1″
│ │ ╰─ Not first block in difficulty adjustment period
│ ╰─── Not first block in halving epoch
╰───── Second cycle

Rare Gro Supply

Total Supply

  • common: 10.4 quadrillion
  • uncommon: 6,929,999
  • rare: 3437
  • epic: 32
  • legendary: 5
  • mythic: 1

Current Supply

  • common: 8.3 quadrillion
  • uncommon: 745,855
  • rare: 369
  • epic: 3
  • legendary: 0
  • mythic: 1

At the moment, even uncommon gros are quite rare. As of this writing, 745,855 uncommon gros have been mined - one per 25.6 groestlcoin in circulation.

Names

Each gro has a name, consisting of the letters A through Z, that get shorter the further into the future the gro was mined. They could start short and get longer, but then all the good, short names would be trapped in the unspendable genesis block.

As an example, 1905530482684727°'s name is "iaiufjszmoba". The name of the last gro to be mined is "a". Every combination of 10 characters or less is out there, or will be out there, someday.

Exotics

Gros may be prized for reasons other than their name or rarity. This might be due to a quality of the number itself, like having an integer square or cube root. Or it might be due to a connection to a historical event, such as gros from block 1,439,424, the block in which SegWit activated, or 10499999999999999°, the last gro that will ever be mined.

Such gros are termed "exotic". Which gros are exotic and what makes them so is subjective. Ordinal theorists are encouraged to seek out exotics based on criteria of their own devising.

Inscriptions

Gros can be inscribed with arbitrary content, creating Groestlcoin-native digital artifacts. Inscribing is done by sending the gro to be inscribed in a transaction that reveals the inscription content on-chain. This content is then inextricably linked to that gro, turning it into an immutable digital artifact that can be tracked, transferred, hoarded, bought, sold, lost, and rediscovered.

Archaeology

Whether or not ordinals are of interest to NFT archaeologists is an open question! Ordinals were in fact created by Gruve-P in 2014 when he mined the Groestlcoin genesis block. In this sense, ordinals, and especially early ordinals, are certainly of historical interest.