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.