Triple

T21953416
Position Surface form Disambiguated ID Type / Status
Subject Lie algebra E542122 entity
Predicate hasExample P1259 FINISHED
Object Witt algebra
The Witt algebra is an infinite-dimensional Lie algebra of derivations of the Laurent polynomial ring, playing a central role in conformal field theory and as the centerless version of the Virasoro algebra.
 E1510866 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: Witt algebra | Statement: [Lie algebra, hasExample, Witt algebra]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Witt algebra
Context triple: [Lie algebra, hasExample, Witt algebra]
  • A. affine Lie algebras
    Affine Lie algebras are infinite-dimensional extensions of finite-dimensional simple Lie algebras that play a central role in representation theory, conformal field theory, and the study of exactly solvable models in mathematical physics.
  • B. Kac–Moody algebras
    Kac–Moody algebras are a broad class of (generally infinite-dimensional) Lie algebras defined by generalized Cartan matrices, encompassing finite-dimensional semisimple Lie algebras and their infinite-dimensional extensions used in representation theory and mathematical physics.
  • C. Weyl algebra
    The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
  • D. Weyl group
    A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
  • E. Onsager algebra
    The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
  • 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: Witt algebra
Triple: [Lie algebra, hasExample, Witt algebra]
Generated description
The Witt algebra is an infinite-dimensional Lie algebra of derivations of the Laurent polynomial ring, playing a central role in conformal field theory and as the centerless version of the Virasoro algebra.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Witt algebra
Target entity description: The Witt algebra is an infinite-dimensional Lie algebra of derivations of the Laurent polynomial ring, playing a central role in conformal field theory and as the centerless version of the Virasoro algebra.
  • A. affine Lie algebras
    Affine Lie algebras are infinite-dimensional extensions of finite-dimensional simple Lie algebras that play a central role in representation theory, conformal field theory, and the study of exactly solvable models in mathematical physics.
  • B. Kac–Moody algebras
    Kac–Moody algebras are a broad class of (generally infinite-dimensional) Lie algebras defined by generalized Cartan matrices, encompassing finite-dimensional semisimple Lie algebras and their infinite-dimensional extensions used in representation theory and mathematical physics.
  • C. Weyl algebra
    The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
  • D. Weyl group
    A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
  • E. Onsager algebra
    The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
  • 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_69e0c47ef0e48190a50e1bcc43f4b3fd completed April 16, 2026, 11:14 a.m.
NER Named-entity recognition batch_69f1243dfb4081909bc7a722843ffea7 completed April 28, 2026, 9:18 p.m.
NED1 Entity disambiguation (via context triple) batch_6a0a670672b481908b92e15245212e64 completed May 18, 2026, 1:10 a.m.
NEDg Description generation batch_6a0a67c29848819080860f13b4c9697b completed May 18, 2026, 1:13 a.m.
NED2 Entity disambiguation (via description) batch_6a0a686a0f208190977890119ffcff79 completed May 18, 2026, 1:16 a.m.
Created at: April 16, 2026, 7:59 p.m.