I will take "Centrist wing of the party" to mean "among the 40% most right wing democratic congressmen per dw-nominate". If it's a real outsider without a dw nominate score, will try to clarify as I go.

(For comparison, Biden was about the 50th percentile in the 11th congress, so this would require someone slightly more conservative than Biden relative to the party average).

"Major presidential candidate" means one of the top three candidates in the primary by delegate shares (conditional on winning at least one state).

(Since this may end up being mildly subjective, I won't bet)