Triple

T22965039
Position Surface form Disambiguated ID Type / Status
Subject Bombieri–Lang conjecture E571015 entity
Predicate generalizes P2372 FINISHED
Object Mordell conjecture NE NERFINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Mordell conjecture | Statement: [Bombieri–Lang conjecture, generalizes, Mordell conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mordell conjecture
Context triple: [Bombieri–Lang conjecture, generalizes, Mordell conjecture]
  • A. Faltings' theorem chosen
    Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
  • B. Mordell–Weil theorem
    The Mordell–Weil theorem is a fundamental result in number theory stating that the group of rational points on an abelian variety (in particular, an elliptic curve) over a number field is finitely generated.
  • C. Bombieri–Lang conjecture
    The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
  • D. Ribet's theorem
    Ribet's theorem is a result in number theory that linked certain modular forms to Galois representations and played a crucial role in the proof of Fermat's Last Theorem.
  • E. Szpiro conjecture
    The Szpiro conjecture is a deep unproven statement in arithmetic geometry about the relationship between the discriminant and conductor of elliptic curves over the rationals, and is known to be essentially equivalent to the abc conjecture.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69e245b212a88190b5259caf51606084 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f181f763688190aab8f444a1a71577 completed April 29, 2026, 3:58 a.m.
Created at: April 17, 2026, 3:47 p.m.