Triple
T7600740
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Pauli matrices |
E179974
|
entity |
| Predicate | basisOf |
P2421
|
FINISHED |
| Object | Lie algebra of SU(2) |
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 of SU(2) | Statement: [Pauli matrices, basisOf, Lie algebra of SU(2)]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lie algebra of SU(2) Context triple: [Pauli matrices, basisOf, Lie algebra of SU(2)]
-
A.
Heisenberg Lie algebra
The Heisenberg Lie algebra is a fundamental nilpotent Lie algebra generated by position and momentum operators with a central element, encoding the canonical commutation relations that underlie quantum mechanics and harmonic analysis.
-
B.
rotation group SU(2)
The rotation group SU(2) is the Lie group of 2×2 unitary matrices with determinant 1 that serves as the double cover of the three-dimensional rotation group SO(3) and underlies the quantum theory of angular momentum and spin.
-
C.
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.
-
D.
SL(2,C)
SL(2,C) is the complex special linear group of 2×2 matrices with determinant 1, which serves as the double cover and spinor representation group of the proper orthochronous Lorentz group in four-dimensional spacetime.
-
E.
Lie algebras
chosen
Lie algebras are algebraic structures used to study continuous symmetries, especially those arising from Lie groups, via a linearized, infinitesimal perspective.
- 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_69c69f3567008190ab01d2ca7b53584a |
completed | March 27, 2026, 3:16 p.m. |
| NER | Named-entity recognition | batch_69c6f9d9c55c8190841f3bf3225c096a |
completed | March 27, 2026, 9:42 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c861b0649c8190b374b5e81f8ba453 |
completed | March 28, 2026, 11:18 p.m. |
Created at: March 27, 2026, 3:53 p.m.