Standard olympiad problems use mod 2 or coloring invariants. Eternica problems use invariants from advanced linear algebra or algebraic topology. For example: "Prove that the winding number of the path never equals zero."
If you stumble upon an archived "Eternica" thread and decide to take the plunge, here is how the community suggests you prepare: eternica aops
Ablations to test: with/without consolidation, with static vs. adaptive curricula, different novelty schedulers. Standard olympiad problems use mod 2 or coloring invariants
4.1. Problem Generator
4.2. Curriculum Manager
4.3. Skill Acquisition and Consolidation 4.4. Evaluation and Self-Play
4.4. Evaluation and Self-Play