Triple

T10991797
Position Surface form Disambiguated ID Type / Status
Subject uniformization theorem E259768 entity
Predicate relatedConcept P37 FINISHED
Object Kleinian groups E259766 NE FINISHED

How this triple was built (2 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: Kleinian groups | Statement: [uniformization theorem, relatedConcept, Kleinian groups]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Kleinian groups
Context triple: [uniformization theorem, relatedConcept, Kleinian groups]
  • A. Kleinian group chosen
    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.
  • B. Sullivan dictionary relating Kleinian groups and complex dynamics
    The Sullivan dictionary relating Kleinian groups and complex dynamics is a conceptual framework that draws deep analogies between the theory of Kleinian groups and the iteration of rational maps, unifying key ideas in geometric group theory and complex dynamical systems.
  • C. Fuchsian group
    A Fuchsian group is a discrete group of isometries of the hyperbolic plane, fundamental in the study of Riemann surfaces, modular forms, and hyperbolic geometry.
  • D. 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.
  • E. Teichmüller theory
    Teichmüller theory is a branch of complex analysis and geometry that studies the deformation spaces of Riemann surfaces and their moduli, often via quasiconformal mappings.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
Created at: April 8, 2026, 9:24 p.m.