Triple
T1234872
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Sophus Lie |
E26524
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object | Lie algebras |
E125772
|
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 algebras | Statement: [Sophus Lie, knownFor, Lie algebras]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lie algebras Context triple: [Sophus Lie, knownFor, Lie algebras]
-
A.
Lie theory
chosen
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.
-
B.
Cartan subalgebras
Cartan subalgebras are maximal abelian subalgebras of a Lie algebra consisting of semisimple elements, fundamental for classifying and understanding the structure of Lie algebras.
-
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.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
-
E.
Cartan decomposition
Cartan decomposition is a fundamental structural result in Lie theory that expresses a Lie algebra or Lie group as a direct sum or product of subspaces or subgroups with specific symmetry properties, widely used in differential geometry and representation theory.
- 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_69a4948571c88190a9191e451e6035fd |
completed | March 1, 2026, 7:33 p.m. |
| NER | Named-entity recognition | batch_69a4be5e421081908f2432528019db25 |
completed | March 1, 2026, 10:31 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ac8a16badc8190b5b603db0ca738cb |
completed | March 7, 2026, 8:27 p.m. |
Created at: March 1, 2026, 7:47 p.m.