Triple

T7338472
Position Surface form Disambiguated ID Type / Status
Subject Jones polynomial E169187 entity
Predicate relatedConjecture P38188 FINISHED
Object 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.
E656686 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: Volume conjecture | Statement: [Jones polynomial, relatedConjecture, Volume conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Volume conjecture
Context triple: [Jones polynomial, relatedConjecture, Volume conjecture]
  • 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. geometrization conjecture
    The geometrization conjecture is a fundamental statement in 3-dimensional topology that classifies all closed 3-manifolds into pieces each admitting one of eight canonical geometric structures, a result proven by Grigori Perelman.
  • C. 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.
  • D. Dehn invariant
    The Dehn invariant is a mathematical quantity in geometry that helps determine whether two polyhedra are scissors-congruent, playing a key role in the solution of Hilbert’s third problem.
  • E. Poincaré conjecture
    The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
  • 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: Volume conjecture
Triple: [Jones polynomial, relatedConjecture, Volume conjecture]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Volume conjecture
Target entity description: 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.
  • 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. geometrization conjecture
    The geometrization conjecture is a fundamental statement in 3-dimensional topology that classifies all closed 3-manifolds into pieces each admitting one of eight canonical geometric structures, a result proven by Grigori Perelman.
  • C. 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.
  • D. Dehn invariant
    The Dehn invariant is a mathematical quantity in geometry that helps determine whether two polyhedra are scissors-congruent, playing a key role in the solution of Hilbert’s third problem.
  • E. Poincaré conjecture
    The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
  • 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.