Triple

T11214924
Position Surface form Disambiguated ID Type / Status
Subject Dehn surgery E265411 entity
Predicate relatedTheorem P49212 FINISHED
Object Lickorish–Wallace theorem
The Lickorish–Wallace theorem is a fundamental result in 3-manifold topology stating that every closed, orientable 3-manifold can be obtained from the 3-sphere by performing Dehn surgery along a link.
E265411 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: Lickorish–Wallace theorem | Statement: [Dehn surgery, relatedTheorem, Lickorish–Wallace theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lickorish–Wallace theorem
Context triple: [Dehn surgery, relatedTheorem, Lickorish–Wallace theorem]
  • A. Lickorish
    Lickorish is a mathematician known for his influential contributions to low-dimensional topology and knot theory.
  • B. Hoste–Thistlethwaite–Weeks knot tables
    The Hoste–Thistlethwaite–Weeks knot tables are comprehensive, systematically generated lists of prime knots (and links) organized by crossing number, widely used as a modern extension and refinement of classical knot tabulations in knot theory.
  • C. 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.
  • D. 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.
  • E. Kauffman polynomial
    The Kauffman polynomial is a two-variable knot invariant in knot theory that generalizes and extends the information captured by the Jones polynomial.
  • 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: Lickorish–Wallace theorem
Triple: [Dehn surgery, relatedTheorem, Lickorish–Wallace theorem]
Generated description
The Lickorish–Wallace theorem is a fundamental result in 3-manifold topology stating that every closed, orientable 3-manifold can be obtained from the 3-sphere by performing Dehn surgery along a link.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lickorish–Wallace theorem
Target entity description: The Lickorish–Wallace theorem is a fundamental result in 3-manifold topology stating that every closed, orientable 3-manifold can be obtained from the 3-sphere by performing Dehn surgery along a link.
  • A. Lickorish
    Lickorish is a mathematician known for his influential contributions to low-dimensional topology and knot theory.
  • B. Hoste–Thistlethwaite–Weeks knot tables
    The Hoste–Thistlethwaite–Weeks knot tables are comprehensive, systematically generated lists of prime knots (and links) organized by crossing number, widely used as a modern extension and refinement of classical knot tabulations in knot theory.
  • C. 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.
  • D. Dehn surgery chosen
    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.
  • E. Kauffman polynomial
    The Kauffman polynomial is a two-variable knot invariant in knot theory that generalizes and extends the information captured by the Jones polynomial.
  • F. None of above.

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.