Triple
T5425648
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | E(n) |
E121355
|
entity |
| Predicate | containsSubgroup |
P10571
|
FINISHED |
| Object | orthogonal group O(n) |
E518473
|
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: orthogonal group O(n) | Statement: [E(n), containsSubgroup, orthogonal group O(n)]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: orthogonal group O(n) Context triple: [E(n), containsSubgroup, orthogonal group O(n)]
-
A.
orthogonal group O(n)
chosen
The orthogonal group O(n) is the group of all n×n real matrices that preserve the standard Euclidean inner product, representing rotations and reflections in n-dimensional space.
-
B.
Euclidean group
The Euclidean group is the group of all distance-preserving transformations of Euclidean space, consisting of rotations, reflections, and translations.
-
C.
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.
-
D.
rotation group SO(3)
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.
-
E.
affine group of R^n
The affine group of ℝⁿ is the group of all invertible affine transformations of n-dimensional real space, combining linear transformations with translations.
- 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_69bd463b58d88190b258261573de9e91 |
completed | March 20, 2026, 1:06 p.m. |
| NER | Named-entity recognition | batch_69bd881598448190a9bb456dee36004b |
completed | March 20, 2026, 5:47 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bf6c548a40819086910fbc39b21e90 |
completed | March 22, 2026, 4:13 a.m. |
Created at: March 20, 2026, 2:06 p.m.