Triple

T23234928
Position Surface form Disambiguated ID Type / Status
Subject orthogonal group O(n+1,2) E581259 entity
Predicate hasSpinCover P151467 FINISHED
Object Spin(n+1,2)
Spin(n+1,2) is the double-cover spin group associated with the (n+3)-dimensional pseudo-orthogonal group of signature (n+1,2), playing a central role in the study of spinors and conformal geometry in that signature.
E1576710 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(n+1,2) | Statement: [orthogonal group O(n+1,2), hasSpinCover, Spin(n+1,2)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Spin(n+1,2)
Context triple: [orthogonal group O(n+1,2), hasSpinCover, Spin(n+1,2)]
  • A. 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.
  • B. 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.
  • C. symplectic group Sp(2n,R)
    The symplectic group Sp(2n,ℝ) is the Lie group of 2n×2n real matrices that preserve a nondegenerate skew-symmetric bilinear form, playing a central role in symplectic geometry and Hamiltonian mechanics.
  • D. SO(2,d-1)
    SO(2,d-1) is the non-compact Lorentz group in (d+1) dimensions that serves as the symmetry group of d-dimensional anti-de Sitter space and plays a central role in AdS/CFT correspondence.
  • 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(n+1,2)
Triple: [orthogonal group O(n+1,2), hasSpinCover, Spin(n+1,2)]
Generated description
Spin(n+1,2) is the double-cover spin group associated with the (n+3)-dimensional pseudo-orthogonal group of signature (n+1,2), playing a central role in the study of spinors and conformal geometry in that signature.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Spin(n+1,2)
Target entity description: Spin(n+1,2) is the double-cover spin group associated with the (n+3)-dimensional pseudo-orthogonal group of signature (n+1,2), playing a central role in the study of spinors and conformal geometry in that signature.
  • A. 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.
  • B. 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.
  • C. symplectic group Sp(2n,R)
    The symplectic group Sp(2n,ℝ) is the Lie group of 2n×2n real matrices that preserve a nondegenerate skew-symmetric bilinear form, playing a central role in symplectic geometry and Hamiltonian mechanics.
  • D. SO(2,d-1)
    SO(2,d-1) is the non-compact Lorentz group in (d+1) dimensions that serves as the symmetry group of d-dimensional anti-de Sitter space and plays a central role in AdS/CFT correspondence.
  • 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: hasSpinCover
Context triple: [orthogonal group O(n+1,2), hasSpinCover, Spin(n+1,2)]
  • A. hasSpin
    Indicates that one entity possesses or exhibits rotational motion or angular momentum.
  • B. hasOpenCoverCondition
    Indicates that a mathematical object satisfies the open cover condition, meaning every open cover of it admits a suitable refinement or subcover meeting the specified requirement.
  • C. hasCoverType
    Indicates that one entity possesses or is associated with a specific type or category of cover.
  • D. hasSpinEffect
    Indicates that one entity causes or exhibits a spinning or rotational effect on another entity.
  • E. 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).
  • 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_69e2460556f88190be1744a84a84173f completed April 17, 2026, 2:39 p.m.
NER Named-entity recognition batch_69f192e8c7548190b53434eeb2620a6e completed April 29, 2026, 5:11 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0c3f59de808190afb414450ac32d0d completed May 19, 2026, 10:45 a.m.
NEDg Description generation batch_6a0c4008c4a881908ad49e733b549036 completed May 19, 2026, 10:48 a.m.
NED2 Entity disambiguation (via description) batch_6a0c40c6562481908689eca2a4997115 completed May 19, 2026, 10:51 a.m.
PD Predicate disambiguation batch_69effcdadec0819092ec1749ee453b4e completed April 28, 2026, 12:18 a.m.
PDg Predicate description generation batch_69f01d8770d081908897c28b04e5faea completed April 28, 2026, 2:37 a.m.
Created at: April 17, 2026, 4:09 p.m.