"""JAM 3 opening instrument (2026-07-23): THE SETTLED LEXICON measured
look-and-say's 6-block census decaying with per-step factor ~0.87 and
ARGUED it is |lambda2|/lambda1 of Conway's 92-element matrix. The
eigenvalue reading makes a falsifiable prediction WITHOUT Conway's
table: an eigenvalue is basis-independent, so EVERY census functional
(2-blocks, 4-blocks, 6-blocks, bare digits) must relax at the SAME
per-step factor. Measured here: consecutive-step total-variation
ratios per census, steps 45..58."""
from itertools import groupby


def las_step(s: str) -> str:
    return "".join(str(len(list(g))) + k for k, g in groupby(s))


def census(s: str, k: int) -> dict:
    counts: dict = {}
    for i in range(len(s) - k + 1):
        b = s[i:i + k]
        counts[b] = counts.get(b, 0) + 1
    total = len(s) - k + 1
    return {b: c / total for b, c in counts.items()}


def tv(p: dict, q: dict) -> float:
    return 0.5 * sum(abs(p.get(x, 0.0) - q.get(x, 0.0)) for x in set(p) | set(q))


def main():
    s = "1"
    hist = {}
    for n in range(1, 59):
        s = las_step(s)
        if n >= 44:
            hist[n] = s
    print("census | per-step TV ratios (geometric mean over steps 45..58)")
    for k in (1, 2, 4, 6):
        prev, ratios, last_tv = None, [], None
        for n in sorted(hist):
            c = census(hist[n], k)
            if prev is not None:
                t = tv(prev, c)
                if last_tv is not None and last_tv > 0:
                    ratios.append(t / last_tv)
                last_tv = t
            prev = c
        gm = 1.0
        for r in ratios:
            gm *= r
        gm **= 1.0 / len(ratios)
        print("  %d-blocks: factor %.4f  (n=%d ratios, min %.3f max %.3f)"
              % (k, gm, len(ratios), min(ratios), max(ratios)))


if __name__ == "__main__":
    main()