Triple

T7011142
Position Surface form Disambiguated ID Type / Status
Subject Karen Vogtmann E162581 entity
Predicate coDeveloperOf P6901 FINISHED
Object 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.
E634851 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: Culler–Vogtmann Outer space | Statement: [Karen Vogtmann, coDeveloperOf, Culler–Vogtmann Outer space]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Culler–Vogtmann Outer space
Context triple: [Karen Vogtmann, coDeveloperOf, Culler–Vogtmann Outer space]
  • A. Dehn complex
    The Dehn complex is a topological construction introduced by Max Dehn in the study of group presentations and decision problems, encoding relations of a group as a 2-dimensional cell complex.
  • B. “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.
  • C. Dehn’s decision problems in group theory
    Dehn’s decision problems in group theory are foundational early 20th-century problems that introduced algorithmic questions about the solvability of word, conjugacy, and isomorphism problems in finitely presented groups, helping launch the field of algorithmic group theory.
  • D. Milnor–Wood inequality
    The Milnor–Wood inequality is a result in differential geometry and topology that bounds the Euler class of flat circle bundles over surfaces, with important implications for foliations and group actions on the circle.
  • E. 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.
  • 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: Culler–Vogtmann Outer space
Triple: [Karen Vogtmann, coDeveloperOf, Culler–Vogtmann Outer space]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Culler–Vogtmann Outer space
Target entity description: 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.
  • A. Dehn complex
    The Dehn complex is a topological construction introduced by Max Dehn in the study of group presentations and decision problems, encoding relations of a group as a 2-dimensional cell complex.
  • B. “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.
  • C. Dehn’s decision problems in group theory
    Dehn’s decision problems in group theory are foundational early 20th-century problems that introduced algorithmic questions about the solvability of word, conjugacy, and isomorphism problems in finitely presented groups, helping launch the field of algorithmic group theory.
  • D. Milnor–Wood inequality
    The Milnor–Wood inequality is a result in differential geometry and topology that bounds the Euler class of flat circle bundles over surfaces, with important implications for foliations and group actions on the circle.
  • E. 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.
  • 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_69c6885a127c8190867b059bdccf13ff completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6dc5729448190af66dbd6f3e8936e completed March 27, 2026, 7:36 p.m.
NED1 Entity disambiguation (via context triple) batch_69c76a4bd424819097e1543ec59979ff completed March 28, 2026, 5:42 a.m.
NEDg Description generation batch_69c76b1ef6f481908f4c4f610328f633 completed March 28, 2026, 5:46 a.m.
NED2 Entity disambiguation (via description) batch_69c76c01679c8190b61f642c23c25ed5 completed March 28, 2026, 5:49 a.m.
Created at: March 27, 2026, 2:34 p.m.