Triple

T26255205
Position Surface form Disambiguated ID Type / Status
Subject Poincaré upper half-plane model E656696 entity
Predicate hasFullIsometryGroup P14251 FINISHED
Object PGL(2,ℝ)
PGL(2,ℝ) is the projective general linear group of 2×2 real matrices modulo nonzero scalar multiples, acting by Möbius transformations on the real projective line and the upper half-plane.
 E656693 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: PGL(2,ℝ) | Statement: [Poincaré upper half-plane model, hasFullIsometryGroup, PGL(2,ℝ)]
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: PGL(2,ℝ)
Triple: [Poincaré upper half-plane model, hasFullIsometryGroup, PGL(2,ℝ)]
Generated description
PGL(2,ℝ) is the projective general linear group of 2×2 real matrices modulo nonzero scalar multiples, acting by Möbius transformations on the real projective line and the upper half-plane.
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: hasFullIsometryGroup
Context triple: [Poincaré upper half-plane model, hasFullIsometryGroup, PGL(2,ℝ)]
  • A. hasIsometryGroup chosen
    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. isMaximallySymmetric
    Indicates that the subject exhibits the highest possible degree of symmetry allowed by the relevant structure, constraints, or context.
  • D. hasAutomorphismGroupContaining
    Indicates that the automorphism group of one mathematical structure includes the other group as a subgroup or component.
  • E. hasAutomorphism
    Indicates that there exists a structure-preserving bijection from an entity to itself that maintains all relevant relations and operations.
  • 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_69ee5b4d25ac819086acb51184602576 completed April 26, 2026, 6:37 p.m.
NER Named-entity recognition batch_69f60dcd2e688190b54e36b0ff0d9187 completed May 2, 2026, 2:44 p.m.
NED1 Entity disambiguation (via context triple) batch_6a1185aaa938819094c6a7f051289d3d completed May 23, 2026, 10:47 a.m.
NEDg Description generation batch_6a11862050608190bf26431a0fb90b07 completed May 23, 2026, 10:49 a.m.
NED2 Entity disambiguation (via description) batch_6a1186c04c2c8190a5e70c9d9a5cbeb8 completed May 23, 2026, 10:51 a.m.
PD Predicate disambiguation batch_69f60b874cc88190a487230abb69efea completed May 2, 2026, 2:34 p.m.
Created at: April 26, 2026, 9:08 p.m.