Triple

T6282492
Position Surface form Disambiguated ID Type / Status
Subject Lie algebra representation E140812 entity
Predicate relatedTo P37 FINISHED
Object Lie group representation E503510 NE 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: Lie group representation | Statement: [Lie algebra representation, relatedTo, Lie group representation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lie group representation
Context triple: [Lie algebra representation, relatedTo, Lie group representation]
  • A. Lie algebra representation
    A Lie algebra representation is a way of expressing a Lie algebra as linear transformations of a vector space, enabling the study of its structure through matrices and linear operators.
  • B. Lie group
    A Lie group is a mathematical structure that is both a smooth manifold and a group, where the group operations are differentiable and used to study continuous symmetries.
  • C. Representations of groups chosen
    Representations of groups is a branch of mathematics that studies how abstract groups can act as linear transformations on vector spaces, typically via homomorphisms into groups of matrices.
  • D. Lie theory
    Lie theory is a branch of mathematics that studies continuous symmetry through Lie groups and Lie algebras, with deep applications in geometry, analysis, and theoretical physics.
  • E. Lorentz group
    The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

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_69c008cd17c8819082b82d3fbeb68047 completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c063f956c08190ae0f198ccbd68b42 completed March 22, 2026, 9:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69c51962132881909a2eccd1203e03c1 completed March 26, 2026, 11:32 a.m.
Created at: March 22, 2026, 4:26 p.m.