the program encodes the last 512 transfers as a binary string: 1 for buy, 0 for sell, ordered by slot. it computes the lempel-ziv complexity of the string — the number of distinct subpatterns the string contains when parsed left to right without repetition. class I strings compress to a single subpattern. class II strings compress to a handful of repeating motifs. class III strings do not compress — every substring is novel, which is the formal definition of randomness. class IV strings compress partially. they contain structure, but the structure is not periodic. the compression ratio ρ = (distinct subpatterns) / (string length) sits in a band between 0.35 and 0.55 for class IV. outside that band, the market is producing a pattern that no collection of independent agents would produce.

surcharge = k · max(0, |ρ − 0.45| − 0.10)² — the quadratic distance from the class IV band, with a dead zone of ±0.10 around the center. inside the band, the surcharge is zero. outside, it grows quadratically. the surcharge is withheld atomically from each transfer via the token-2022 hook return value, routed to a vault pda, and distributed to holders weighted by anti-periodicity: the lempel-ziv complexity of each holder's own transfer history. holders who transfer aperiodically — high complexity, high individuality — receive the most. holders whose transfer history is periodic — low complexity, bot-like regularity — receive the least.