Triple
T3072662
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Annals of Mathematics Studies |
E64059
|
entity |
| Predicate | hasNotableWork |
P4
|
FINISHED |
| Object |
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.
|
E325284
|
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: Hyperbolic Manifolds and Discrete Groups | Statement: [Annals of Mathematics Studies, hasNotableWork, Hyperbolic Manifolds and Discrete Groups]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hyperbolic Manifolds and Discrete Groups Context triple: [Annals of Mathematics Studies, hasNotableWork, Hyperbolic Manifolds and Discrete Groups]
-
A.
Milnor–Wood inequality
The Milnor–Wood inequality is a result in differential geometry and topology that bounds the Euler class of flat circle bundles over surfaces, with important implications for foliations and group actions on the circle.
-
B.
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.
-
C.
Dehn’s decision problems in group theory
Dehn’s decision problems in group theory are foundational early 20th-century problems that introduced algorithmic questions about the solvability of word, conjugacy, and isomorphism problems in finitely presented groups, helping launch the field of algorithmic group theory.
-
D.
Dehn complex
The Dehn complex is a topological construction introduced by Max Dehn in the study of group presentations and decision problems, encoding relations of a group as a 2-dimensional cell complex.
-
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. 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: Hyperbolic Manifolds and Discrete Groups Triple: [Annals of Mathematics Studies, hasNotableWork, Hyperbolic Manifolds and Discrete Groups]
Generated description
"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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hyperbolic Manifolds and Discrete Groups Target entity description: "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.
-
A.
Milnor–Wood inequality
The Milnor–Wood inequality is a result in differential geometry and topology that bounds the Euler class of flat circle bundles over surfaces, with important implications for foliations and group actions on the circle.
-
B.
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.
-
C.
Dehn’s decision problems in group theory
Dehn’s decision problems in group theory are foundational early 20th-century problems that introduced algorithmic questions about the solvability of word, conjugacy, and isomorphism problems in finitely presented groups, helping launch the field of algorithmic group theory.
-
D.
Dehn complex
The Dehn complex is a topological construction introduced by Max Dehn in the study of group presentations and decision problems, encoding relations of a group as a 2-dimensional cell complex.
-
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. 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_69ad857a8aec8190bfdfd9c14554ac5a |
completed | March 8, 2026, 2:19 p.m. |
| NER | Named-entity recognition | batch_69ada14e372c81908c25c7f3e7e0c864 |
completed | March 8, 2026, 4:18 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b1f8828c488190877902a6c2dfcb5e |
completed | March 11, 2026, 11:19 p.m. |
| NEDg | Description generation | batch_69b1f930321081908f98aa5f9b8ba611 |
completed | March 11, 2026, 11:22 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69b1f9ad0b148190b98f93699598dd1e |
completed | March 11, 2026, 11:24 p.m. |
Created at: March 8, 2026, 3:02 p.m.