Triple

T11214928
Position Surface form Disambiguated ID Type / Status
Subject Dehn surgery E265411 entity
Predicate canProduce P5771 FINISHED
Object Seifert fibered spaces
Seifert fibered spaces are three-dimensional manifolds that can be decomposed into a disjoint union of circles arranged in a highly structured, fibered way over a two-dimensional orbifold.
E911225 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: Seifert fibered spaces | Statement: [Dehn surgery, canProduce, Seifert fibered spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Seifert fibered spaces
Context triple: [Dehn surgery, canProduce, Seifert fibered spaces]
  • A. 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.
  • 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. Thurston hyperbolization theorem
    The Thurston hyperbolization theorem is a fundamental result in 3-manifold topology that characterizes when certain 3-manifolds admit complete hyperbolic structures, forming a cornerstone of Thurston’s geometrization program.
  • D. Culler–Vogtmann Outer space
    Culler–Vogtmann Outer space is a topological space that parametrizes marked metric graphs, serving as an analogue of Teichmüller space for studying the outer automorphism group of a free group.
  • E. “Braids, Links, and Mapping Class Groups”
    “Braids, Links, and Mapping Class Groups” is a foundational monograph in low-dimensional topology that systematically develops the theory of braids, links, and mapping class groups and their interrelations.
  • 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: Seifert fibered spaces
Triple: [Dehn surgery, canProduce, Seifert fibered spaces]
Generated description
Seifert fibered spaces are three-dimensional manifolds that can be decomposed into a disjoint union of circles arranged in a highly structured, fibered way over a two-dimensional orbifold.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Seifert fibered spaces
Target entity description: Seifert fibered spaces are three-dimensional manifolds that can be decomposed into a disjoint union of circles arranged in a highly structured, fibered way over a two-dimensional orbifold.
  • A. 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.
  • 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. Thurston hyperbolization theorem
    The Thurston hyperbolization theorem is a fundamental result in 3-manifold topology that characterizes when certain 3-manifolds admit complete hyperbolic structures, forming a cornerstone of Thurston’s geometrization program.
  • D. Culler–Vogtmann Outer space
    Culler–Vogtmann Outer space is a topological space that parametrizes marked metric graphs, serving as an analogue of Teichmüller space for studying the outer automorphism group of a free group.
  • E. “Braids, Links, and Mapping Class Groups”
    “Braids, Links, and Mapping Class Groups” is a foundational monograph in low-dimensional topology that systematically develops the theory of braids, links, and mapping class groups and their interrelations.
  • 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_69d6aac59460819089b9848b27f57848 completed April 8, 2026, 7:21 p.m.
NER Named-entity recognition batch_69d7e8e8eef48190932a85784ce15c86 completed April 9, 2026, 5:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69e49762e3188190ba3c0e01cf04f6a1 completed April 19, 2026, 8:50 a.m.
NEDg Description generation batch_69e49d37989881909c7e75ddfff06726 completed April 19, 2026, 9:15 a.m.
NED2 Entity disambiguation (via description) batch_69e49f41a1f8819087cc15527dc7ff63 completed April 19, 2026, 9:24 a.m.
Created at: April 8, 2026, 9:30 p.m.