"""THE SETTLED LEXICON - instrument (2026-07-22, walked from THE POOR
LANGUAGE's frontier question: "is the democratic flatness the shadow
of Conway's computed atomic abundances, or a step-35 transient?").
Method: walk look-and-say (seed "1") far past step 35, sampling the
6-block census at steps 35..58. If the census DRIFTS, the flatness
was weather; if it FREEZES (total-variation distance between samples
falling toward 0 while distinct-block count and the 90%-coverage
crew hold), the poor language is a settled tongue - the finite
shadow of the cosmological theorem's converging element abundances.
Every figure printed is COMPUTED; the mechanism named is ARGUED."""
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):
    counts: dict = {}
    for i in range(len(s) - 5):
        b = s[i:i + 6]
        counts[b] = counts.get(b, 0) + 1
    total = len(s) - 5
    freq = {b: c / total for b, c in counts.items()}
    ranked = sorted(freq.values(), reverse=True)
    mass, crew = 0.0, 0
    for f in ranked:
        mass += f
        crew += 1
        if mass >= 0.90:
            break
    return freq, len(counts), crew


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


def main():
    s = "1"
    samples = [35, 40, 45, 50, 54, 58]
    prev = None
    print("step |  length   | distinct 6-blocks | 90% crew | TV vs prev sample")
    results = []
    for n in range(1, samples[-1] + 1):
        s = las_step(s)
        if n in samples:
            freq, distinct, crew = census(s)
            d = tv(prev, freq) if prev is not None else float("nan")
            print("  %2d | %9d | %17d | %8d | %s"
                  % (n, len(s), distinct, crew,
                     ("%.5f" % d) if prev is not None else "   -"))
            results.append((n, distinct, crew, d))
            prev = freq
    # the verdict gates (pre-declared): settled means the census
    # freezes - TV falling monotonically toward ~0 across the last
    # three gaps, while distinct count and crew move by at most a
    # hair (<=3%) between the deepest two samples.
    tvs = [d for _, _, _, d in results[1:]]
    a, b = results[-2], results[-1]
    settled = (tvs[-1] < tvs[0] and tvs[-1] < 0.01
               and abs(b[1] - a[1]) <= 0.03 * a[1]
               and abs(b[2] - a[2]) <= max(3, 0.03 * a[2]))
    print("\nTV trail (gaps between samples):",
          " -> ".join("%.5f" % d for d in tvs))
    print("VERDICT:", "SETTLED - the poor language is a converged tongue,"
          " not a transient" if settled else
          "STILL DRIFTING at step 58 - the flatness may be weather")


if __name__ == "__main__":
    main()