Triple

T12014653
Position Surface form Disambiguated ID Type / Status
Subject J. Lee, Introduction to Smooth Manifolds E285992 entity
Predicate relatedWork P37 FINISHED
Object John M. Lee, Riemannian Manifolds: An Introduction to Curvature
"John M. Lee, Riemannian Manifolds: An Introduction to Curvature" is a widely used graduate-level textbook that develops the theory of Riemannian geometry with an emphasis on curvature and its geometric and analytic consequences.
E960691 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: John M. Lee, Riemannian Manifolds: An Introduction to Curvature | Statement: [J. Lee, Introduction to Smooth Manifolds, relatedWork, John M. Lee, Riemannian Manifolds: An Introduction to Curvature]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: John M. Lee, Riemannian Manifolds: An Introduction to Curvature
Context triple: [J. Lee, Introduction to Smooth Manifolds, relatedWork, John M. Lee, Riemannian Manifolds: An Introduction to Curvature]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Riemannian manifolds
    Riemannian manifolds are smooth manifolds equipped with an inner product on each tangent space that allows one to measure lengths, angles, and curvature in a curved geometric setting.
  • E. Vorlesungen über Differentialgeometrie
    Vorlesungen über Differentialgeometrie is a classic multi-volume textbook on differential geometry by Wilhelm Blaschke that significantly shaped the development and teaching of the subject in the 20th century.
  • 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: John M. Lee, Riemannian Manifolds: An Introduction to Curvature
Triple: [J. Lee, Introduction to Smooth Manifolds, relatedWork, John M. Lee, Riemannian Manifolds: An Introduction to Curvature]
Generated description
"John M. Lee, Riemannian Manifolds: An Introduction to Curvature" is a widely used graduate-level textbook that develops the theory of Riemannian geometry with an emphasis on curvature and its geometric and analytic consequences.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: John M. Lee, Riemannian Manifolds: An Introduction to Curvature
Target entity description: "John M. Lee, Riemannian Manifolds: An Introduction to Curvature" is a widely used graduate-level textbook that develops the theory of Riemannian geometry with an emphasis on curvature and its geometric and analytic consequences.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Riemannian manifolds
    Riemannian manifolds are smooth manifolds equipped with an inner product on each tangent space that allows one to measure lengths, angles, and curvature in a curved geometric setting.
  • E. Vorlesungen über Differentialgeometrie
    Vorlesungen über Differentialgeometrie is a classic multi-volume textbook on differential geometry by Wilhelm Blaschke that significantly shaped the development and teaching of the subject in the 20th century.
  • 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_69d6ab45a368819084fce08bf0dc3705 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d903d884488190b4450a98088208ef completed April 10, 2026, 2:06 p.m.
NED1 Entity disambiguation (via context triple) batch_69f48b4535f48190ac5b2cabb4daf4af completed May 1, 2026, 11:15 a.m.
NEDg Description generation batch_69f490cb9328819095481a4d0fb0c625 completed May 1, 2026, 11:38 a.m.
NED2 Entity disambiguation (via description) batch_69f495cc50908190aab4f8ca64c66ef3 completed May 1, 2026, noon
Created at: April 8, 2026, 9:46 p.m.