Triple

T8733456
Position Surface form Disambiguated ID Type / Status
Subject Hasse–Weil zeta function E207313 entity
Predicate satisfies P4233 FINISHED
Object Weil conjectures for varieties over finite fields 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 for varieties over finite fields | Statement: [Hasse–Weil zeta function, satisfies, Weil conjectures for varieties over finite fields]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Weil conjectures for varieties over finite fields
Context triple: [Hasse–Weil zeta function, satisfies, Weil conjectures for varieties over finite fields]
  • 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. Standard Conjectures on Algebraic Cycles
    The Standard Conjectures on Algebraic Cycles are a set of deep, still unproven hypotheses in algebraic geometry that aim to provide a foundational theory of algebraic cycles and their cohomological properties, underpinning much of the modern theory of motives.
  • C. Hodge–Riemann bilinear relations
    The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
  • D. 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.
  • E. Chevalley’s theorem in algebraic geometry
    Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
  • 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_69ca8358e4008190898471a59b96c301 completed March 30, 2026, 2:06 p.m.
NER Named-entity recognition batch_69cc5d2a26988190acfda17f232e610a completed March 31, 2026, 11:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69cf292d71ec819082095cb7b8b2d39c completed April 3, 2026, 2:42 a.m.
Created at: March 30, 2026, 6:37 p.m.