Triple
T6475519
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Dennis Sullivan |
E146060
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object |
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.
|
E596065
|
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: Sullivan dictionary relating Kleinian groups and complex dynamics | Statement: [Dennis Sullivan, notableFor, Sullivan dictionary relating Kleinian groups and complex dynamics]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Sullivan dictionary relating Kleinian groups and complex dynamics Context triple: [Dennis Sullivan, notableFor, Sullivan dictionary relating Kleinian groups and complex dynamics]
-
A.
Dynamics in One Complex Variable
Dynamics in One Complex Variable is a foundational graduate-level textbook by John Milnor that introduces and develops the theory of complex dynamical systems, particularly the iteration of rational maps on the Riemann sphere.
-
B.
Milnor–Thurston kneading theory
Milnor–Thurston kneading theory is a mathematical framework in one-dimensional dynamical systems that encodes the combinatorial behavior of interval maps to study their dynamics and entropy.
-
C.
Thurston’s classification of surface diffeomorphisms
Thurston’s classification of surface diffeomorphisms is a foundational theorem in low-dimensional topology that categorizes self-maps of surfaces into periodic, reducible, or pseudo-Anosov types, profoundly influencing the study of 3-manifolds and dynamical systems.
-
D.
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.
-
E.
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.
- 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: Sullivan dictionary relating Kleinian groups and complex dynamics Triple: [Dennis Sullivan, notableFor, Sullivan dictionary relating Kleinian groups and complex dynamics]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Sullivan dictionary relating Kleinian groups and complex dynamics Target entity description: 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.
-
A.
Dynamics in One Complex Variable
Dynamics in One Complex Variable is a foundational graduate-level textbook by John Milnor that introduces and develops the theory of complex dynamical systems, particularly the iteration of rational maps on the Riemann sphere.
-
B.
Milnor–Thurston kneading theory
Milnor–Thurston kneading theory is a mathematical framework in one-dimensional dynamical systems that encodes the combinatorial behavior of interval maps to study their dynamics and entropy.
-
C.
Thurston’s classification of surface diffeomorphisms
Thurston’s classification of surface diffeomorphisms is a foundational theorem in low-dimensional topology that categorizes self-maps of surfaces into periodic, reducible, or pseudo-Anosov types, profoundly influencing the study of 3-manifolds and dynamical systems.
-
D.
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.
-
E.
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.
- 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_69c008fec7408190af7b146dc63d9750 |
completed | March 22, 2026, 3:21 p.m. |
| NER | Named-entity recognition | batch_69c06a341360819082f2b5496a1a68b0 |
completed | March 22, 2026, 10:16 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c653a595b881909e5d3cb781ad5ad4 |
completed | March 27, 2026, 9:53 a.m. |
| NEDg | Description generation | batch_69c6553c17bc81908719ecc7db9e3960 |
completed | March 27, 2026, 10 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c655f4ee5c81909620e732b72ee694 |
completed | March 27, 2026, 10:03 a.m. |
Created at: March 22, 2026, 4:50 p.m.