Triple

T21953456
Position Surface form Disambiguated ID Type / Status
Subject universal enveloping algebra E542123 entity
Predicate associatedGradedAlgebra P62051 FINISHED
Object symmetric algebra of the Lie algebra LITERAL FINISHED

How this triple was built (2 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: symmetric algebra of the Lie algebra | Statement: [universal enveloping algebra, associatedGradedAlgebra, symmetric algebra of the Lie algebra]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: associatedGradedAlgebra
Context triple: [universal enveloping algebra, associatedGradedAlgebra, symmetric algebra of the Lie algebra]
  • A. associatedGradedIs chosen
    Indicates that one mathematical object is the associated graded object (e.g., graded structure derived from a filtration) of another.
  • B. generatedAsQAlgebraBy
    Indicates that something is produced or derived through a specific QA (question-answering) algebraic process or construction.
  • C. hasLieAlgebra
    Indicates that one mathematical structure is associated with, or gives rise to, a specific Lie algebra capturing its infinitesimal or tangent-level structure.
  • D. associatedQuadraticForm
    Indicates that one mathematical object (such as a bilinear form, matrix, or linear operator) is linked to or determines a specific quadratic form derived from it.
  • E. isRingTheoreticAnalogueOf
    Indicates that one concept in ring theory serves as the structural or conceptual counterpart of another notion from a different mathematical context.
  • F. None of above.

Provenance (3 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.
PD Predicate disambiguation batch_69e6f601f2188190893bcdde0cf58ad6 completed April 21, 2026, 3:58 a.m.
Created at: April 16, 2026, 7:59 p.m.