Triple
T11098848
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Clebsch–Gordan coefficients |
E262449
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | SO(3) Lie group |
E174596
|
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: SO(3) Lie group | Statement: [Clebsch–Gordan coefficients, relatedTo, SO(3) Lie group]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: SO(3) Lie group Context triple: [Clebsch–Gordan coefficients, relatedTo, SO(3) Lie group]
-
A.
rotation group SO(3)
chosen
The rotation group SO(3) is the group of all rotations in three-dimensional space, represented by 3×3 orthogonal matrices with determinant 1, and plays a central role in classical mechanics, quantum mechanics, and geometry.
-
B.
special orthogonal group SO(n)
The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
-
C.
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.
-
D.
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.
-
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_69d6aa9a40d88190a373e2c7e48285db |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d79a0c46308190889b94c23ebaca62 |
completed | April 9, 2026, 12:22 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e3e7eca9bc8190b43bae081d97d804 |
completed | April 18, 2026, 8:22 p.m. |
Created at: April 8, 2026, 9:27 p.m.