Triple
T2652956
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Whitney approximation theorem |
E53941
|
entity |
| Predicate | standardReference |
P33736
|
FINISHED |
| Object |
J. Munkres, Elementary Differential Topology
"J. Munkres, Elementary Differential Topology" is a classic introductory textbook that rigorously develops the foundations of differential topology, including topics such as smooth manifolds, transversality, and approximation theorems.
|
E288084
|
NE FINISHED |
How this triple was built (4 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: J. Munkres, Elementary Differential Topology | Statement: [Whitney approximation theorem, standardReference, J. Munkres, Elementary Differential Topology]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: J. Munkres, Elementary Differential Topology Context triple: [Whitney approximation theorem, standardReference, J. Munkres, Elementary Differential Topology]
-
A.
M. Hirsch, Differential Topology
*Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
-
B.
J. Lee, Introduction to Smooth Manifolds
*J. Lee, Introduction to Smooth Manifolds* is a widely used graduate-level textbook that provides a rigorous and accessible introduction to the theory of smooth manifolds and differential topology.
-
C.
Topology from the Differentiable Viewpoint
"Topology from the Differentiable Viewpoint" is a classic introductory monograph on differential topology that presents key concepts such as smooth manifolds, vector bundles, and characteristic classes in a concise and accessible style.
-
D.
Topologie (with Heinz Hopf)
"Topologie" is a foundational 1935 textbook on general topology co-authored by Pavel Alexandrov and Heinz Hopf that helped shape the modern development of the field.
-
E.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: J. Munkres, Elementary Differential Topology Triple: [Whitney approximation theorem, standardReference, J. Munkres, Elementary Differential Topology]
Generated description
"J. Munkres, Elementary Differential Topology" is a classic introductory textbook that rigorously develops the foundations of differential topology, including topics such as smooth manifolds, transversality, and approximation theorems.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: J. Munkres, Elementary Differential Topology Target entity description: "J. Munkres, Elementary Differential Topology" is a classic introductory textbook that rigorously develops the foundations of differential topology, including topics such as smooth manifolds, transversality, and approximation theorems.
-
A.
M. Hirsch, Differential Topology
*Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
-
B.
J. Lee, Introduction to Smooth Manifolds
*J. Lee, Introduction to Smooth Manifolds* is a widely used graduate-level textbook that provides a rigorous and accessible introduction to the theory of smooth manifolds and differential topology.
-
C.
Topology from the Differentiable Viewpoint
"Topology from the Differentiable Viewpoint" is a classic introductory monograph on differential topology that presents key concepts such as smooth manifolds, vector bundles, and characteristic classes in a concise and accessible style.
-
D.
Topologie (with Heinz Hopf)
"Topologie" is a foundational 1935 textbook on general topology co-authored by Pavel Alexandrov and Heinz Hopf that helped shape the modern development of the field.
-
E.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
- F. None of above. chosen
Provenance (5 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_69ab495e192081909c77b622e8e7e15a |
completed | March 6, 2026, 9:38 p.m. |
| NER | Named-entity recognition | batch_69abd93197f48190b04faf358b503204 |
completed | March 7, 2026, 7:52 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69afa052c91c8190abfd49dbc62a4448 |
completed | March 10, 2026, 4:38 a.m. |
| NEDg | Description generation | batch_69afa0fef4c481908db42628cd6e72fe |
completed | March 10, 2026, 4:41 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69afa1fc3884819094503650206ec788 |
completed | March 10, 2026, 4:45 a.m. |
Created at: March 6, 2026, 9:53 p.m.