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.