This market resolves to YES if, before January 1, 2031, a major mathematical breakthrough or resolution regarding aliquot sequences is published and verified. Otherwise, it resolves to NO.

Resolution Criteria

Any of the following milestones will trigger a YES resolution:

1. Resolution of Catalan–Dickson or Guy–Selfridge: A general proof settling either the Catalan–Dickson conjecture (proving all aliquot sequences are bounded) or the Guy–Selfridge conjecture (formally proving that unbounded aliquot sequences do exist).

2. Proof of an Unbounded Sequence: A verified mathematical proof demonstrating that at least one specific starting integer $n$ produces an infinite/unbounded aliquot trajectory.

3. Resolution of a Lehmer Five Seed: Definitive proof that the sequence for 276, 552, 564, 660, or 966 either terminates (hits 1/0) or enters a periodic cycle (amicable pair or sociable cycle).

Verification & Rules

The proof or resolution must be published in a peer-reviewed mathematics journal, an accepted arXiv pre-print acknowledged by the mathematical community, or officially confirmed by major math news outlets (e.g., Quanta Magazine*, AMS, or MAA).

Simple computational progress (e.g., reaching higher digit limits for 276 without proving termination or a cycle) does NOT count as a YES.

Trader Responsibility: If a qualifying breakthrough occurs, traders are asked to post a comment with a link to the paper/announcement. If no verified proof is posted by the close date, this market will resolve NO.