Triple
T6295448
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lie bracket |
E141120
|
entity |
| Predicate | codomain |
P7031
|
FINISHED |
| Object | Lie algebra |
E542122
|
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 algebra | Statement: [Lie bracket, codomain, Lie algebra]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lie algebra Context triple: [Lie bracket, codomain, Lie algebra]
-
A.
Lie algebras
chosen
Lie algebras are algebraic structures used to study continuous symmetries, especially those arising from Lie groups, via a linearized, infinitesimal perspective.
-
B.
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.
-
C.
Lie algebroid
A Lie algebroid is a geometric structure that generalizes Lie algebras and tangent bundles, encoding infinitesimal symmetries on manifolds via a vector bundle with a Lie bracket and an anchor map.
-
D.
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.
-
E.
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.
- 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_69c008cdf2ac8190bb640c94478fb4ed |
completed | March 22, 2026, 3:20 p.m. |
| NER | Named-entity recognition | batch_69c06439a6908190b0a8ebf426d3ca02 |
completed | March 22, 2026, 9:50 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c6385c26f08190952d810a82b9236f |
completed | March 27, 2026, 7:57 a.m. |
Created at: March 22, 2026, 4:27 p.m.