Triple

T19231168
Position Surface form Disambiguated ID Type / Status
Subject Runge approximation theorem E480873 entity
Predicate relatedTo P37 FINISHED
Object Oka–Weil theorem NE NERFINISHED

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: Oka–Weil theorem | Statement: [Runge approximation theorem, relatedTo, Oka–Weil theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Oka–Weil theorem
Context triple: [Runge approximation theorem, relatedTo, Oka–Weil theorem]
  • A. Oka–Weil theorem chosen
    The Oka–Weil theorem is a fundamental result in several complex variables that extends Runge’s approximation theorem by characterizing when holomorphic functions on certain compact sets in complex manifolds can be uniformly approximated by global holomorphic functions.
  • B. Grothendieck–Lefschetz theorem
    The Grothendieck–Lefschetz theorem is a fundamental result in algebraic geometry that extends Lefschetz-type hyperplane theorems to a broad scheme-theoretic and cohomological setting, relating the geometry and Picard groups of a variety to those of its hyperplane sections.
  • C. Grothendieck–Riemann–Roch theorem
    The Grothendieck–Riemann–Roch theorem is a fundamental result in algebraic geometry that generalizes the classical Riemann–Roch theorem by relating pushforwards in K-theory to pushforwards in cohomology via characteristic classes.
  • D. 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.
  • E. Hirzebruch–Riemann–Roch theorem
    The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8e8ccb8f48190ad420098e74fb1db completed April 10, 2026, 12:10 p.m.
NER Named-entity recognition batch_69e5fa9ce5e081909df994841ce476d5 completed April 20, 2026, 10:06 a.m.
Created at: April 10, 2026, 1:25 p.m.