The most famous Eternica AoPS thread, titled "Eternica's Ladder (No finite solutions allowed)," became legendary because it remained unsolved for 47 days—an eternity for the active AoPS community. Notable IMO medalists allegedly attempted the problem, only to claim the problem was "ill-posed" or "paradoxical."
Eternica (the user) defended the problem by introducing a new lemma, informally dubbed the "Eternica Fixed Point Theorem" (not to be confused with Brouwer's), which suggested that in a sufficiently complex logical system, the act of searching for a solution creates the solution. eternica aops
If you are searching for Eternica AoPS content to solve yourself, here is how to identify an authentic Eternica-style challenge: The most famous Eternica AoPS thread, titled "Eternica's
Ablations to test: with/without consolidation, with static vs. adaptive curricula, different novelty schedulers. Ablations to test: with/without consolidation