Triple

T1523330
Position Surface form Disambiguated ID Type / Status
Subject Millennium Prize Problem E32278 entity
Predicate includes P1393 FINISHED
Object Birch and Swinnerton-Dyer Conjecture E175567 NE FINISHED

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: Birch and Swinnerton-Dyer Conjecture | Statement: [Millennium Prize Problem, includes, Birch and Swinnerton-Dyer Conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Birch and Swinnerton-Dyer Conjecture
Context triple: [Millennium Prize Problem, includes, Birch and Swinnerton-Dyer Conjecture]
  • A. Birch and Swinnerton-Dyer Conjecture chosen
    The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
  • B. Hodge Conjecture
    The Hodge Conjecture is a major unsolved problem in algebraic geometry that predicts which cohomology classes on a non-singular projective complex variety arise from algebraic subvarieties.
  • C. Fermat's Last Theorem
    Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
  • D. Riemann hypothesis
    The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
  • E. Hardy–Littlewood conjectures
    The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69a885e9b0ac819093a9806ad0efc82c completed March 4, 2026, 7:20 p.m.
NER Named-entity recognition batch_69a90800433c8190b23ae2860493a16e completed March 5, 2026, 4:35 a.m.
NED1 Entity disambiguation (via context triple) batch_69ad401616ec81908edd9dcb9f4a0184 completed March 8, 2026, 9:23 a.m.
Created at: March 4, 2026, 7:26 p.m.