Triple

T6456474
Position Surface form Disambiguated ID Type / Status
Subject Lie group E142004 entity
Predicate hasExample P1259 FINISHED
Object special orthogonal group SO(n) E524430 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: special orthogonal group SO(n) | Statement: [Lie group, hasExample, special orthogonal group SO(n)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: special orthogonal group SO(n)
Context triple: [Lie group, hasExample, special orthogonal group SO(n)]
  • A. special orthogonal group SO(n) chosen
    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.
  • B. orthogonal group O(n)
    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.
  • C. 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.
  • D. orthogonal group O(n+1,2)
    The orthogonal group O(n+1,2) is the Lie group of linear transformations preserving a nondegenerate quadratic form of signature (n+1,2), playing a central role in conformal and Lie sphere geometry.
  • 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_69c008d2f91c8190a8178767a35e08fc completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c069d639ec8190bb0a806da4118440 completed March 22, 2026, 10:14 p.m.
NED1 Entity disambiguation (via context triple) batch_69c64bdc4e808190a7c24b963ab0aa30 completed March 27, 2026, 9:20 a.m.
Created at: March 22, 2026, 4:48 p.m.