entropie
a token that measures its own disorder.
every holder list is a probability distribution. each wallet holds a share of supply, and a share is a probability. the entropie program keeps the shannon entropy of that distribution as a live on-chain number, updated inside the transfer itself. no oracle, no indexer, no operator. the mint knows how spread out it is the way a gas knows its temperature.
the number is H, measured in nats. divided by its ceiling it becomes J, a reading between zero and one. at zero, one wallet is the whole float. at one, the float is perfectly level across every holder. nothing pushes the number anywhere. it is simply known, on chain, at all times, and anyone can read it.
a transfer changes exactly two balances, so the program never recomputes the whole sum. it subtracts the two stale terms, adds the two fresh ones, and writes the result back in the same transaction that moved the tokens. if the transfer lands, the measurement landed with it. constant work per transfer, whether the mint has fifty holders or five hundred thousand.
everything on this page is one of two things: that mathematics drawn exactly, or live market data read once per second. below, the same measurement is pointed outward, at the flow across the fifty most traded tokens on solana, compressed into a single number. when the entropie mint is live, its own market cap and liquidity join the page through the same one second wire.
the second law is patient. so is this page.
the quantity
let p be the vector of holder shares, pi = balancei / supply. the shares sum to one, so the holder list is already a probability distribution and needs no normalising.
H grows as the float spreads. its ceiling for n holders is ln n, reached only when every holder is level. dividing by the ceiling removes the holder count from the reading:
the two ends
| J = 0 | one wallet is the whole float. there is nothing to be uncertain about, so the entropy is exactly zero. |
| J = 1 | the float is perfectly level across every holder. this holds at any n — five holders level and five hundred thousand holders level both read one. |
constant work per transfer
a transfer moves tokens between exactly two accounts, so only two terms of the sum change. the program subtracts the two stale terms, adds the two fresh ones, and stores the result:
where t(b) = −(b/S)·ln(b/S)
this is not an approximation. the incremental result is bit-identical to recomputing the whole sum, because subtraction and addition of the same real terms is exact arithmetic on the same quantity. the cost is two logarithms per transfer and does not grow with the holder count.
what is not claimed
| not a price | J describes the shape of the holder list and nothing else. a high reading is not a signal to buy and a low one is not a signal to sell. |
| not fairness | an even distribution can be manufactured by splitting one holding across many wallets. J cannot tell wallets apart from people, and nothing on chain can. |
| not safety | the measurement changes nothing about the token's behaviour. it is a thermometer, not a thermostat. |
the needle
the chart on the index page applies the same formula outward: p becomes each token's share of the last hour's volume across the fifty most traded tokens on solana. the numbers are read from a public market index, once per second, and the reading is computed in the page. when the feed cannot be reached the line stops rather than inventing a value.