Triple

T22965051
Position Surface form Disambiguated ID Type / Status
Subject Bombieri–Lang conjecture E571015 entity
Predicate influencedBy P9 FINISHED
Object Weil conjectures on curves E244835 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: Weil conjectures on curves | Statement: [Bombieri–Lang conjecture, influencedBy, Weil conjectures on curves]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Weil conjectures on curves
Context triple: [Bombieri–Lang conjecture, influencedBy, Weil conjectures on 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. Shafarevich conjecture for abelian varieties
    The Shafarevich conjecture for abelian varieties is a finiteness statement predicting that, over a number field, there are only finitely many isomorphism classes of abelian varieties with good reduction outside a fixed finite set of places, a result ultimately proved by Faltings.
  • 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–Lefschetz trace formula
    The Grothendieck–Lefschetz trace formula is a fundamental result in algebraic geometry that expresses the number of rational points of a variety over a finite field in terms of traces of Frobenius acting on its étale cohomology groups.
  • 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_69e245b212a88190b5259caf51606084 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f181f763688190aab8f444a1a71577 completed April 29, 2026, 3:58 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0bca22caa88190889e965c78477a96 completed May 19, 2026, 2:25 a.m.
Created at: April 17, 2026, 3:47 p.m.