Rare sats

Every bitcoin is 100,000,000 satoshis, and ordinal theory numbers each one in the order it was mined. Some of those numbers land on something: the first sat of a block, a sat mined by Satoshi, a sat that paid for a pizza. Sat hunters find them, inscribe on them, trade them. This is every kind Mantel recognises. Paste a Bitcoin address into the search and the wallet's outputs are checked against all of it; open any inscription and its own sat is named.

Rodarmor rarity

Casey Rodarmor's original index, from ordinal theory. Sats are numbered in the order they were mined, so the first sat of each recurring event in Bitcoin's schedule is its own class.

Uncommon: The first sat of every block.Supply One per block, about 964,000 so farsat 5,000,000,000
Rare: The first sat of every difficulty adjustment, every 2,016 blocks.Supply 478 so farsat 10,080,000,000,000
Epic: The first sat of every halving, every 210,000 blocks.Supply 4 so farsat 1,050,000,000,000,000
Legendary: The first sat of every cycle, where a difficulty adjustment and a halving land on the same block, every 1,260,000 blocks.Supply None yet; the first arrives at block 1,260,000, around 2032
Mythic: Sat 0, the first sat of the genesis block.Supply 1sat 0

Black

The mirror of the index: where Rodarmor sats open an event, black sats close the one before it. The sat right before each boundary.

Black uncommon: The last sat of every block.Supply One per blocksat 4,999,999,999
Black rare: The last sat before a difficulty adjustment.Supply 478 so farsat 10,079,999,999,999
Black epic: The last sat before a halving.Supply 4 so farsat 1,049,999,999,999,999
Black legendary: The last sat before a cycle.Supply None yet

Early blocks

Where a sat was mined, when the network was a handful of people.

Vintage: Mined in the first 1,000 blocks, January 2009.Supply 5,000,000,000,000 sats (50,000 BTC)
Nakamoto: Mined in one of the 21,953 blocks attributed to Satoshi by the Patoshi pattern, Sergio Demian Lerner's analysis of the ExtraNonce field in early coinbases.Supply About 1,097,650 BTC, almost all never moved
Block 9: Mined in block 9, the first block whose coins ever moved: Satoshi sent 10 of them to Hal Finney on 12 January 2009.Supply 5,000,000,000 sats (50 BTC)sat 45,000,000,000
Block 9 450x: The first bitcoin of block 9, sats 45,000,000,000 to 45,099,999,999, the coins in that first transaction.Supply 100,000,000 sats (1 BTC)
Block 78: Mined in block 78, the first block mined by someone other than Satoshi: Hal Finney.Supply 5,000,000,000 sats (50 BTC)sat 390,000,000,000
Block 286: Mined in block 286, the second block whose coins Satoshi sent on.Supply 5,000,000,000 sats (50 BTC)

Traced through transactions

Sats that sat in one historic transaction, followed forward as the coins split and moved, using the ordinal rule that sats travel first-in first-out. Mantel holds every range; each list sums to its transaction to the sat.

Pizza: The 10,000 BTC that bought two pizzas on 22 May 2010.Supply 1,000,000,000,000 sats (10,000 BTC), 828 ranges
JPEG: The 500 BTC paid for a desktop wallpaper on 24 February 2010, the first bitcoin ever traded for an image (tx 298a46fd…d18d, block 42,373).Supply 50,000,000,000 sats (500 BTC), 10 ranges
Hitman: The 1,670 BTC Dread Pirate Roberts paid on 31 March 2013 to have a blackmailer killed (tx 4a0a5b60…5601, block 228,940). The hit never happened; the payment did.Supply 167,000,000,000 sats (1,670 BTC), 6,200 ranges
Silk Road: The 29,656.5 BTC seized from Silk Road and sold in the US Marshals' first auction, 27 June 2014, delivered 1 July (tx 9e95c3c3…b0c3, block 308,777).Supply 2,965,651,306,529 sats, 405,534 ranges

The number itself

Nothing to do with when or where. The digits.

Palindrome: The sat number reads the same backwards.Supply About 142 millionsat 1,234,554,321
Uniform palinception: A palindrome that splits into equal segments, each itself a palindrome of at least two digits.Supply Rare; counted by handsat 121,131,121
Perfect palinception: A palindrome made of one palindromic segment repeated.Supply A few hundredsat 997,999,979,999,799
Alpha: The first sat of a whole bitcoin: the number ends in eight zeros.Supply One per bitcoin, about 20 millionsat 12,300,000,000
Omega: The last sat of a whole bitcoin: the number ends in 99999999.Supply One per bitcoinsat 12,399,999,999
Fibonacci: The sat number is a Fibonacci number. Seventy-four of them fit under the last sat.Supply 74sat 1,548,008,755,920
1, 2 or 3 digits: The number uses only one, two or three distinct digits, over at least five places. One digit is the rarest: 11111, 222222, and so on.Supply Few, fewer, fewest
Binary: Only zeros and ones, at least five places.Supply Raresat 1,011,010,110
Sequential: The digits step up or down by one all the way, at least five places: 456789, 987654321.Supply Raresat 123,456,789
Name palindrome: Every sat has a name, base 26 of its distance from the last sat ever mined (sat 0 is nvtdijuwxlp, the last is a). A name that reads the same backwards.Supply Rare; the names shorten as the numbers rise

For sale

How Mantel checks

A wallet's outputs are read from ordinals.com, which reports the sat ranges each output holds. Everything in the first three sections and the last is arithmetic on those numbers: which block a sat was mined in follows from the subsidy schedule, so no index is needed. The traced lists are held in full, four hundred thousand ranges, and every range in a wallet is checked against them. Up to three hundred outputs are checked per address; the section says how many it looked at. Not named, because no clean trace exists: the sats of the second hitman payments, and anything defined by an exchange rather than the chain.

Sources: ordinal theory (Casey Rodarmor), the Patoshi block analysis (Sergio Demian Lerner, curated by Jameson Lopp), transaction traces by Sating, and the chain itself.