Triple

T5425329
Position Surface form Disambiguated ID Type / Status
Subject William Thurston E121348 entity
Predicate doctoralThesisTitle P1860 FINISHED
Object Foliations of Three-Manifolds Which Are Circle Bundles
"Foliations of Three-Manifolds Which Are Circle Bundles" is William Thurston’s influential 1972 doctoral dissertation in geometric topology, where he developed foundational ideas about the structure and classification of foliations on 3-manifolds.
E518461 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: Foliations of Three-Manifolds Which Are Circle Bundles | Statement: [William Thurston, doctoralThesisTitle, Foliations of Three-Manifolds Which Are Circle Bundles]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Foliations of Three-Manifolds Which Are Circle Bundles
Context triple: [William Thurston, doctoralThesisTitle, Foliations of Three-Manifolds Which Are Circle Bundles]
  • A. Wirtinger presentation of knot groups
    The Wirtinger presentation of knot groups is a classical method in knot theory that describes the fundamental group of a knot complement using generators and relations derived from a knot diagram.
  • B. Dehn surgery
    Dehn surgery is a fundamental operation in 3-manifold topology that modifies a 3-dimensional manifold by cutting out a solid torus and gluing it back in a different way, playing a central role in the classification and study of 3-manifolds.
  • C. Hyperbolic Manifolds and Discrete Groups
    "Hyperbolic Manifolds and Discrete Groups" is a foundational mathematical monograph that develops the theory of hyperbolic geometry and its deep connections with discrete group actions and low-dimensional topology.
  • D. 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.
  • E. Milnor fibration
    Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
  • 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: Foliations of Three-Manifolds Which Are Circle Bundles
Triple: [William Thurston, doctoralThesisTitle, Foliations of Three-Manifolds Which Are Circle Bundles]
Generated description
"Foliations of Three-Manifolds Which Are Circle Bundles" is William Thurston’s influential 1972 doctoral dissertation in geometric topology, where he developed foundational ideas about the structure and classification of foliations on 3-manifolds.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Foliations of Three-Manifolds Which Are Circle Bundles
Target entity description: "Foliations of Three-Manifolds Which Are Circle Bundles" is William Thurston’s influential 1972 doctoral dissertation in geometric topology, where he developed foundational ideas about the structure and classification of foliations on 3-manifolds.
  • A. Wirtinger presentation of knot groups
    The Wirtinger presentation of knot groups is a classical method in knot theory that describes the fundamental group of a knot complement using generators and relations derived from a knot diagram.
  • B. Dehn surgery
    Dehn surgery is a fundamental operation in 3-manifold topology that modifies a 3-dimensional manifold by cutting out a solid torus and gluing it back in a different way, playing a central role in the classification and study of 3-manifolds.
  • C. Hyperbolic Manifolds and Discrete Groups
    "Hyperbolic Manifolds and Discrete Groups" is a foundational mathematical monograph that develops the theory of hyperbolic geometry and its deep connections with discrete group actions and low-dimensional topology.
  • D. 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.
  • E. Milnor fibration
    Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
  • 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_69bd463b58d88190b258261573de9e91 completed March 20, 2026, 1:06 p.m.
NER Named-entity recognition batch_69bd881598448190a9bb456dee36004b completed March 20, 2026, 5:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69bf3abfc7e88190b8f0a31b61c33973 completed March 22, 2026, 12:41 a.m.
NEDg Description generation batch_69bf3b592a08819090e2873bcf4e797f completed March 22, 2026, 12:44 a.m.
NED2 Entity disambiguation (via description) batch_69bf3c0b9e5481909101eccbd55f24b2 completed March 22, 2026, 12:47 a.m.
Created at: March 20, 2026, 2:06 p.m.