Triple

T6397028
Position Surface form Disambiguated ID Type / Status
Subject AdS isometry group SO(2,d) E143965 entity
Predicate hasUniversalCover P70392 FINISHED
Object Spin(2,d)
Spin(2,d) is the double-covering spin group of SO(2,d), serving as the relevant symmetry group for spinor fields in (d+1)-dimensional anti-de Sitter space.
E590885 NE FINISHED

How this triple was built (5 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: Spin(2,d) | Statement: [AdS isometry group SO(2,d), hasUniversalCover, Spin(2,d)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Spin(2,d)
Context triple: [AdS isometry group SO(2,d), hasUniversalCover, Spin(2,d)]
  • A. 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.
  • 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. 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. Poincaré group
    The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
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: Spin(2,d)
Triple: [AdS isometry group SO(2,d), hasUniversalCover, Spin(2,d)]
Generated description
Spin(2,d) is the double-covering spin group of SO(2,d), serving as the relevant symmetry group for spinor fields in (d+1)-dimensional anti-de Sitter space.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Spin(2,d)
Target entity description: Spin(2,d) is the double-covering spin group of SO(2,d), serving as the relevant symmetry group for spinor fields in (d+1)-dimensional anti-de Sitter space.
  • A. 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.
  • 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. 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. Poincaré group
    The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
  • E. 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.
  • F. None of above. chosen
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: hasUniversalCover
Context triple: [AdS isometry group SO(2,d), hasUniversalCover, Spin(2,d)]
  • A. hasCoverFeature
    Indicates that one entity serves as a prominent or featured element on the cover of another entity (such as a publication, product, or media item).
  • B. hasCoverType
    Indicates that one entity possesses or is associated with a specific type or category of cover.
  • C. hasCoverage
    Indicates that one entity provides insurance or protection coverage for another entity or subject.
  • D. isUniversal
    Indicates that the relationship or property holds for all relevant entities or cases without exception.
  • E. mayCover
    Indicates that one entity is permitted or able to extend over, include, or provide coverage for another entity, either partially or fully.
  • F. None of above. chosen

Provenance (7 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_69c008db906c819096f3597d55d95432 completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c068953968819083a94f5de3e11819 completed March 22, 2026, 10:09 p.m.
NED1 Entity disambiguation (via context triple) batch_69c6389bd9f48190af9811cf8cee124e completed March 27, 2026, 7:58 a.m.
NEDg Description generation batch_69c63beaa5408190b4421f49634f3df1 completed March 27, 2026, 8:12 a.m.
NED2 Entity disambiguation (via description) batch_69c63c5f7d508190bd263822cea1b782 completed March 27, 2026, 8:14 a.m.
PD Predicate disambiguation batch_69c060f25c088190b433f78553ff1d84 completed March 22, 2026, 9:36 p.m.
PDg Predicate description generation batch_69c0623d23448190a75cf5d802fc0a02 completed March 22, 2026, 9:42 p.m.
Created at: March 22, 2026, 4:35 p.m.