No counterexample was found in the recorded finite check, and the review left the claim unresolved.
Methodology
From a data pattern to a research note.
The pipeline separates generation, finite-data validation, and mathematical review so that each kind of evidence remains visible.
The sequence
Five recorded stages
Generate a precise candidate
The generator explores LMFDB data for patterns, then formulates a falsifiable statement with hypotheses, object family, ordering, invariants, and an explicit notion of counterexample.
Check for duplicates
A normalized logical form and lexical comparison are used to avoid presenting the same candidate repeatedly. Duplicate detection is a practical safeguard, not a proof of mathematical equivalence.
Search finite LMFDB data independently
A validation stage constructs its own database search over a large portion of LMFDB, records the tested scope and object count, and looks for counterexamples. The goal is to check that the prediction made at step 1 generalizes when the dataset is about 50 times larger. A pass means only that none was found inside that finite scope.
Review literature, proof, and disproof
A separate review looks for nearby results and attempts a proof or disproof with some of the strongest AI models (currently gpt-5.6-sol pro). It records the closest known work, unresolved gap, and confidence in its classification—not a probability that the conjecture is true.
Interest
A separate review on the resulting conjectures tries to estimate the interest of the results in number theory by checking the consequences it would have on known results or human-made conjectures.
Status guide
How to read the labels
Status records the pipeline’s latest classification. It should always be read together with the verification level and the note itself.
Verification level
How far the recorded process went
LMFDB tested & reviewed
The finite check was followed by a separate literature and proof-or-disproof review.