Triple

T8733504
Position Surface form Disambiguated ID Type / Status
Subject Hasse bound for elliptic curves E207314 entity
Predicate isSpecialCaseOf P2372 FINISHED
Object Weil conjectures for curves E244835 NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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: Weil conjectures for curves | Statement: [Hasse bound for elliptic curves, isSpecialCaseOf, Weil conjectures for curves]

Disambiguation candidates (1 decision)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Weil conjectures for curves
Context triple: [Hasse bound for elliptic curves, isSpecialCaseOf, Weil conjectures for curves]
  • A. Weil conjectures chosen
    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.
  • B. Hasse–Weil bound for abelian varieties
    The Hasse–Weil bound for abelian varieties is a fundamental result in arithmetic geometry that gives sharp estimates for the number of rational points on abelian varieties over finite fields in terms of their dimension and the field size.
  • C. Hasse bound for elliptic curves
    The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
  • D. Hurwitz bound on automorphism groups of curves
    The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
  • E. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

Stage Batch ID Job type Status
creating batch_69ca8358e4008190898471a59b96c301 elicitation completed
NER batch_69cc5d2a26988190acfda17f232e610a ner completed
NED1 batch_69cf5174db7881908597d5dc472adde9 ned_source_triple completed
Created at: March 30, 2026, 6:37 p.m.