Triple

T11215038
Position Surface form Disambiguated ID Type / Status
Subject Dehn twist E265413 entity
Predicate appearsIn P795 FINISHED
Object Dehn–Lickorish theorem
The Dehn–Lickorish theorem is a fundamental result in low-dimensional topology stating that the mapping class group of a closed, orientable surface is generated by finitely many Dehn twists.
E912779 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: Dehn–Lickorish theorem | Statement: [Dehn twist, appearsIn, Dehn–Lickorish theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Dehn–Lickorish theorem
Context triple: [Dehn twist, appearsIn, Dehn–Lickorish theorem]
  • A. 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.
  • B. Dehn lemma
    The Dehn lemma is a fundamental result in 3-manifold topology that gives conditions under which a loop on the boundary of a 3-manifold bounds an embedded disk in the manifold.
  • 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. Lickorish
    Lickorish is a mathematician known for his influential contributions to low-dimensional topology and knot theory.
  • E. 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.
  • 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: Dehn–Lickorish theorem
Triple: [Dehn twist, appearsIn, Dehn–Lickorish theorem]
Generated description
The Dehn–Lickorish theorem is a fundamental result in low-dimensional topology stating that the mapping class group of a closed, orientable surface is generated by finitely many Dehn twists.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Dehn–Lickorish theorem
Target entity description: The Dehn–Lickorish theorem is a fundamental result in low-dimensional topology stating that the mapping class group of a closed, orientable surface is generated by finitely many Dehn twists.
  • A. 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.
  • B. Dehn lemma
    The Dehn lemma is a fundamental result in 3-manifold topology that gives conditions under which a loop on the boundary of a 3-manifold bounds an embedded disk in the manifold.
  • 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. Lickorish
    Lickorish is a mathematician known for his influential contributions to low-dimensional topology and knot theory.
  • E. 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.
  • 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_69e4ad1c57908190a5c65ea4738722e3 completed April 19, 2026, 10:23 a.m.
NEDg Description generation batch_69e4b1ee74748190a33449ce1b92813e completed April 19, 2026, 10:43 a.m.
NED2 Entity disambiguation (via description) batch_69e4b3d23b18819096f3a11aecc732bd completed April 19, 2026, 10:52 a.m.
Created at: April 8, 2026, 9:30 p.m.