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.