Triple

T11215229
Position Surface form Disambiguated ID Type / Status
Subject Dehn function E265418 entity
Predicate connectedTo P37 FINISHED
Object Gromov hyperbolic group
A Gromov hyperbolic group is a finitely generated group whose Cayley graph exhibits negative curvature–like properties, leading to rich geometric, dynamical, and algorithmic behavior.
E911231 NE FINISHED

How this triple was built (4 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: Gromov hyperbolic group | Statement: [Dehn function, connectedTo, Gromov hyperbolic group]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gromov hyperbolic group
Context triple: [Dehn function, connectedTo, Gromov hyperbolic group]
  • A. geometric group theory
    Geometric group theory is a branch of mathematics that studies groups by interpreting them as geometric objects and analyzing their actions on spaces using tools from geometry and topology.
  • B. Hyperbolic Manifolds and Discrete Groups
    "Hyperbolic Manifolds and Discrete Groups" is a foundational mathematical monograph that develops the theory of hyperbolic geometry and its deep connections with discrete group actions and low-dimensional topology.
  • C. Kleinian group
    A Kleinian group is a discrete subgroup of Möbius transformations acting on hyperbolic 3-space, central to the study of Riemann surfaces, complex dynamics, and low-dimensional topology.
  • D. Dehn function
    The Dehn function is a mathematical tool in geometric group theory that measures the complexity of filling loops with discs in a space or group, quantifying the difficulty of solving the word problem.
  • E. Culler–Vogtmann Outer space
    Culler–Vogtmann Outer space is a topological space that parametrizes marked metric graphs, serving as an analogue of Teichmüller space for studying the outer automorphism group of a free group.
  • 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: Gromov hyperbolic group
Triple: [Dehn function, connectedTo, Gromov hyperbolic group]
Generated description
A Gromov hyperbolic group is a finitely generated group whose Cayley graph exhibits negative curvature–like properties, leading to rich geometric, dynamical, and algorithmic behavior.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gromov hyperbolic group
Target entity description: A Gromov hyperbolic group is a finitely generated group whose Cayley graph exhibits negative curvature–like properties, leading to rich geometric, dynamical, and algorithmic behavior.
  • A. geometric group theory
    Geometric group theory is a branch of mathematics that studies groups by interpreting them as geometric objects and analyzing their actions on spaces using tools from geometry and topology.
  • B. Hyperbolic Manifolds and Discrete Groups
    "Hyperbolic Manifolds and Discrete Groups" is a foundational mathematical monograph that develops the theory of hyperbolic geometry and its deep connections with discrete group actions and low-dimensional topology.
  • C. Kleinian group
    A Kleinian group is a discrete subgroup of Möbius transformations acting on hyperbolic 3-space, central to the study of Riemann surfaces, complex dynamics, and low-dimensional topology.
  • D. Dehn function
    The Dehn function is a mathematical tool in geometric group theory that measures the complexity of filling loops with discs in a space or group, quantifying the difficulty of solving the word problem.
  • E. Culler–Vogtmann Outer space
    Culler–Vogtmann Outer space is a topological space that parametrizes marked metric graphs, serving as an analogue of Teichmüller space for studying the outer automorphism group of a free group.
  • F. None of above. chosen

Provenance (5 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_69d6aac59460819089b9848b27f57848 completed April 8, 2026, 7:21 p.m.
NER Named-entity recognition batch_69d7e8e8eef48190932a85784ce15c86 completed April 9, 2026, 5:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69e49762e3188190ba3c0e01cf04f6a1 completed April 19, 2026, 8:50 a.m.
NEDg Description generation batch_69e49d37989881909c7e75ddfff06726 completed April 19, 2026, 9:15 a.m.
NED2 Entity disambiguation (via description) batch_69e49f41a1f8819087cc15527dc7ff63 completed April 19, 2026, 9:24 a.m.
Created at: April 8, 2026, 9:30 p.m.