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.