"""JAM 5: does share*sqrt(ln N) actually approach 1/2, or is it still
falling past the point the old checkpoint list could see?

Reuses van_eck_counting_shadow.census() untouched (same recurrence,
same per-step assertion Z(N) = 1 + D(N-1)) and simply asks it for
checkpoints the original script never printed: 100M and 200M. No new
logic, no edits to the audited instrument -- only a wider horizon.
"""

from math import log, sqrt

from van_eck_counting_shadow import census


def main() -> None:
    checkpoints = [50_000_000, 100_000_000, 200_000_000]
    rows = census(200_000_000, checkpoints)
    print("terms | zero share | share*sqrt(ln N) | max zero gap")
    prev = None
    for terms, zeros, _lagged, gap in rows:
        share = zeros / terms
        stat = share * sqrt(log(terms))
        delta = "" if prev is None else f" | delta {stat - prev:+.7f}"
        print(f"{terms:>12,} | {share:>10.7f} | {stat:>16.7f} |"
              f" {gap:>12,}{delta}")
        prev = stat


if __name__ == "__main__":
    main()