Triple

T33985557
Position Surface form Disambiguated ID Type / Status
Subject Siegel upper half-space E871400 entity
Predicate hasIsotropyGroup P140368 FINISHED
Object unitary group U(g)
The unitary group U(g) is the group of g×g complex matrices that preserve the standard Hermitian inner product, playing a central role in complex geometry and representation theory.
 E2077708 NE FINISHED

How this triple was built (3 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: unitary group U(g) | Statement: [Siegel upper half-space, hasIsotropyGroup, unitary group U(g)]
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: unitary group U(g)
Triple: [Siegel upper half-space, hasIsotropyGroup, unitary group U(g)]
Generated description
The unitary group U(g) is the group of g×g complex matrices that preserve the standard Hermitian inner product, playing a central role in complex geometry and representation theory.
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: hasIsotropyGroup
Context triple: [Siegel upper half-space, hasIsotropyGroup, unitary group U(g)]
  • A. hasIsometryGroup
    Indicates that one entity possesses or is associated with a particular isometry group describing all distance-preserving transformations of that entity.
  • B. isMaximalSymmetryGroupOf
    Indicates that a group represents the largest possible symmetry group for a given object or structure, such that no strictly larger symmetry group of that object exists containing it.
  • C. hasAutomorphismGroupContaining chosen
    Indicates that the automorphism group of one mathematical structure includes the other group as a subgroup or component.
  • D. isIsotropicWithRespectTo
    Indicates that one entity exhibits identical properties or behavior in all directions relative to, or when measured with respect to, another specified frame, medium, or reference.
  • E. usesSymmetryGroup
    Indicates that one entity employs or is based on a particular symmetry group in its structure, behavior, or formulation.
  • F. None of above.

Provenance (6 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_69f3499e964c8190b674b03f6f791b4b completed April 30, 2026, 12:22 p.m.
NER Named-entity recognition batch_69f71fb1ab3881908e2f7c0e6f23db49 completed May 3, 2026, 10:13 a.m.
NED1 Entity disambiguation (via context triple) batch_6a3692dc1a948190bba6b5c7824a9a40 completed June 20, 2026, 1:17 p.m.
NEDg Description generation batch_6a3694ea32d48190bee74e8717d79e8e completed June 20, 2026, 1:26 p.m.
NED2 Entity disambiguation (via description) batch_6a3695dcf1748190b4a465bf69162128 completed June 20, 2026, 1:30 p.m.
PD Predicate disambiguation batch_69f71cc6397881909aaad37a9daa8a7e completed May 3, 2026, 10 a.m.
Created at: May 1, 2026, 1:50 a.m.