Triple

T7743558
Position Surface form Disambiguated ID Type / Status
Subject Birch and Swinnerton-Dyer Conjecture E175567 entity
Predicate relatedTo P37 FINISHED
Object Hasse–Weil conjecture E680776 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: Hasse–Weil conjecture | Statement: [Birch and Swinnerton-Dyer Conjecture, relatedTo, Hasse–Weil conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hasse–Weil conjecture
Context triple: [Birch and Swinnerton-Dyer Conjecture, relatedTo, Hasse–Weil conjecture]
  • A. Taniyama–Shimura–Weil conjecture
    The Taniyama–Shimura–Weil conjecture, now the modularity theorem, asserts that every elliptic curve over the rational numbers is modular and played a central role in the proof of Fermat’s Last Theorem.
  • B. Birch and Swinnerton-Dyer Conjecture
    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.
  • C. Tate Conjecture chosen
    The Tate Conjecture is a major open problem in arithmetic geometry that predicts a deep connection between algebraic cycles on varieties over finite fields and their Galois-invariant étale cohomology classes.
  • D. Ramanujan–Petersson conjecture
    The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
  • E. Weil conjectures
    The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
  • 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_69c6995f9c60819092e386192bd63c6f completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c70388d58081909aad2c03b4501e78 completed March 27, 2026, 10:24 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8c7c63c688190ac257a738759d59f completed March 29, 2026, 6:33 a.m.
Created at: March 27, 2026, 4:07 p.m.