entropiea 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 over a short wire. below, the same measurement is pointed outward, at the flow across a fixed basket of twenty heavily 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 wire.
waiting for the first read…
the second law is patient. so is this page.
docs — the measurement, exactly.
## the quantity
let wallet i hold share pᵢ of the circulating float, so Σ pᵢ = 1. the program keeps
H is shannon entropy over the holder distribution. its ceiling for n holders is ln n, reached only when every holder has exactly the same share. dividing by the ceiling gives the needle:
J = 0 — one wallet is the whole float. J = 1 — the float is perfectly level. in between is every real token that has ever existed.
## the update rule
a transfer moves amount t from wallet a to wallet b. only two terms of the sum change, so the program computes
subtract the two stale terms, add the two fresh ones, write H′ back in the same transaction that moved the tokens. if the transfer lands, the measurement landed with it. the work is constant per transfer — fifty holders or five hundred thousand, the cost is the same four logarithms.
## what is exact and what is market data
sections 02 and 03 of the index are that mathematics drawn exactly, running on the bars you can see — every H and J printed there is computed from those sixteen numbers and nothing else. section 01 is live market data: 24h volumes for a fixed basket of twenty heavily traded solana tokens, read from dexscreener roughly every ten seconds, turned into shares, and pushed through the same formula. the two never mix.
## reading it
the needle, the gas and the transfer all print their inputs next to their outputs, so every number on this page can be checked by hand with a calculator and patience. when the entropie mint is live its market cap and liquidity join through the same wire, and the CA printed on the index is the only official one.
no hype, no empty promises. just code, transparency, and verifiable deployment.
notes — short ones, in no hurry.
on gases
a gas does not vote on its temperature. no molecule is in charge of it, no committee publishes it; it is simply a property of how the motion is spread. that is the posture entropie takes toward its holder list. the number is not an opinion about the token. it is the token, seen from one particular angle.
why nats, not bits
log base e instead of base 2. the physics convention, not the computing one — on purpose. bits count questions; nats measure disorder. a holder list is not a quiz.
on the whale
when one wallet swallows the float, J falls toward zero and says so, publicly, in the same transaction that did the swallowing. entropie cannot stop a whale. it can only make sure the whale is measured the instant it eats. sunlight, at constant cost.
the second law
closed systems drift toward disorder. markets are not closed and drift wherever they like — which is exactly why a live reading beats a promise. the page does not predict the needle. it watches it, with you.
the second law is patient. so is this page.