Triple

T20690819
Position Surface form Disambiguated ID Type / Status
Subject Witten–Reshetikhin–Turaev invariant E508543 entity
Predicate relatedTo P37 FINISHED
Object Turaev–Viro invariant
The Turaev–Viro invariant is a 3-dimensional topological quantum field theory invariant of compact 3-manifolds constructed via state-sum models using quantum 6j-symbols.
E1445347 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: Turaev–Viro invariant | Statement: [Witten–Reshetikhin–Turaev invariant, relatedTo, Turaev–Viro invariant]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Turaev–Viro invariant
Context triple: [Witten–Reshetikhin–Turaev invariant, relatedTo, Turaev–Viro invariant]
  • A. Witten–Reshetikhin–Turaev invariant
    The Witten–Reshetikhin–Turaev invariant is a quantum invariant of 3-manifolds and links derived from Chern–Simons theory and quantum groups, playing a central role in low-dimensional topology and quantum topology.
  • B. 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.
  • C. Khovanov homology
    Khovanov homology is a powerful link invariant in knot theory that lifts the Jones polynomial to a graded homology theory, providing stronger topological information than the polynomial alone.
  • D. Volume conjecture
    The Volume conjecture is a proposed deep link between quantum knot invariants and hyperbolic geometry, asserting that the asymptotic behavior of the colored Jones polynomial of a knot determines the hyperbolic volume of its complement.
  • E. Jones polynomial
    The Jones polynomial is a powerful knot invariant in topology that assigns to each knot or link a Laurent polynomial, enabling the distinction of many knots that are indistinguishable by classical invariants.
  • 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: Turaev–Viro invariant
Triple: [Witten–Reshetikhin–Turaev invariant, relatedTo, Turaev–Viro invariant]
Generated description
The Turaev–Viro invariant is a 3-dimensional topological quantum field theory invariant of compact 3-manifolds constructed via state-sum models using quantum 6j-symbols.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Turaev–Viro invariant
Target entity description: The Turaev–Viro invariant is a 3-dimensional topological quantum field theory invariant of compact 3-manifolds constructed via state-sum models using quantum 6j-symbols.
  • A. Witten–Reshetikhin–Turaev invariant
    The Witten–Reshetikhin–Turaev invariant is a quantum invariant of 3-manifolds and links derived from Chern–Simons theory and quantum groups, playing a central role in low-dimensional topology and quantum topology.
  • B. 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.
  • C. Khovanov homology
    Khovanov homology is a powerful link invariant in knot theory that lifts the Jones polynomial to a graded homology theory, providing stronger topological information than the polynomial alone.
  • D. Volume conjecture
    The Volume conjecture is a proposed deep link between quantum knot invariants and hyperbolic geometry, asserting that the asymptotic behavior of the colored Jones polynomial of a knot determines the hyperbolic volume of its complement.
  • E. Jones polynomial
    The Jones polynomial is a powerful knot invariant in topology that assigns to each knot or link a Laurent polynomial, enabling the distinction of many knots that are indistinguishable by classical invariants.
  • 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_69e0b4c1ed408190b72dd26b1e33f8a1 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e6c10d83548190a52b9ef84c8f9205 completed April 21, 2026, 12:13 a.m.
NED1 Entity disambiguation (via context triple) batch_6a08d7e43a3c81909f63e63e30e9c435 completed May 16, 2026, 8:47 p.m.
NEDg Description generation batch_6a08d91216bc8190909e0e37f6d5e612 completed May 16, 2026, 8:52 p.m.
NED2 Entity disambiguation (via description) batch_6a08d99214b48190b0ffba4026d3fa39 completed May 16, 2026, 8:54 p.m.
Created at: April 16, 2026, 12:08 p.m.