Triple
T7338443
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jones polynomial |
E169187
|
entity |
| Predicate | invariantUnder |
P4235
|
FINISHED |
| Object |
Reidemeister moves
Reidemeister moves are the three local diagrammatic transformations in knot theory that characterize when two knot or link diagrams represent the same topological knot.
|
E656683
|
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: Reidemeister moves | Statement: [Jones polynomial, invariantUnder, Reidemeister moves]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Reidemeister moves Context triple: [Jones polynomial, invariantUnder, Reidemeister moves]
-
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 twist
A Dehn twist is a fundamental type of self-homeomorphism of a surface obtained by cutting along a simple closed curve, twisting one side by 360 degrees, and gluing it back, playing a central role in low-dimensional topology and the study of mapping class groups.
-
C.
Conway skein triple (L₊, L₋, L₀)
The Conway skein triple (L₊, L₋, L₀) is a standard configuration of three related link diagrams used in knot theory to express how a link invariant, such as the Conway polynomial, changes under local crossing modifications.
-
D.
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
-
E.
Conway notation for knots
Conway notation for knots is a mathematical system introduced by John H. Conway that encodes knot and link diagrams into concise symbolic expressions to classify and study them.
- 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: Reidemeister moves Triple: [Jones polynomial, invariantUnder, Reidemeister moves]
Generated description
Reidemeister moves are the three local diagrammatic transformations in knot theory that characterize when two knot or link diagrams represent the same topological knot.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Reidemeister moves Target entity description: Reidemeister moves are the three local diagrammatic transformations in knot theory that characterize when two knot or link diagrams represent the same topological knot.
-
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 twist
A Dehn twist is a fundamental type of self-homeomorphism of a surface obtained by cutting along a simple closed curve, twisting one side by 360 degrees, and gluing it back, playing a central role in low-dimensional topology and the study of mapping class groups.
-
C.
Conway skein triple (L₊, L₋, L₀)
The Conway skein triple (L₊, L₋, L₀) is a standard configuration of three related link diagrams used in knot theory to express how a link invariant, such as the Conway polynomial, changes under local crossing modifications.
-
D.
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
-
E.
Conway notation for knots
Conway notation for knots is a mathematical system introduced by John H. Conway that encodes knot and link diagrams into concise symbolic expressions to classify and study them.
- 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_69c68a57710481909f0c1f3c6ebdb6f2 |
completed | March 27, 2026, 1:47 p.m. |
| NER | Named-entity recognition | batch_69c6f0d599c88190875514eae7084f8d |
completed | March 27, 2026, 9:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c7ef266fd0819096cf3ece3fff6b90 |
completed | March 28, 2026, 3:09 p.m. |
| NEDg | Description generation | batch_69c7efa4f5148190842f30988cbea94c |
completed | March 28, 2026, 3:11 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c7f0092bac819080ded1863f99290a |
completed | March 28, 2026, 3:13 p.m. |
Created at: March 27, 2026, 3:04 p.m.