Triple
T10931405
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Nolan Wallach |
E258214
|
entity |
| Predicate | hasWrittenWork |
P4
|
FINISHED |
| Object |
Symplectic Geometry and Fourier Analysis
"Symplectic Geometry and Fourier Analysis" is a mathematical work by Nolan Wallach that explores the interplay between symplectic geometry, representation theory, and Fourier-analytic methods.
|
E893439
|
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: Symplectic Geometry and Fourier Analysis | Statement: [Nolan Wallach, hasWrittenWork, Symplectic Geometry and Fourier Analysis]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Symplectic Geometry and Fourier Analysis Context triple: [Nolan Wallach, hasWrittenWork, Symplectic Geometry and Fourier Analysis]
-
A.
Introduction to Symplectic Topology
Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
-
B.
Fourier restriction theory
Fourier restriction theory is a branch of harmonic analysis that studies when and how the Fourier transform of a function can be meaningfully restricted to lower-dimensional subsets such as curves or surfaces.
-
C.
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
-
D.
McDuff–Salamon theory of J-holomorphic curves
The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
-
E.
Kähler geometry
Kähler geometry is a branch of differential geometry studying complex manifolds equipped with a compatible symplectic form and Riemannian metric, leading to rich interactions between complex, symplectic, and Riemannian geometry.
- 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: Symplectic Geometry and Fourier Analysis Triple: [Nolan Wallach, hasWrittenWork, Symplectic Geometry and Fourier Analysis]
Generated description
"Symplectic Geometry and Fourier Analysis" is a mathematical work by Nolan Wallach that explores the interplay between symplectic geometry, representation theory, and Fourier-analytic methods.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Symplectic Geometry and Fourier Analysis Target entity description: "Symplectic Geometry and Fourier Analysis" is a mathematical work by Nolan Wallach that explores the interplay between symplectic geometry, representation theory, and Fourier-analytic methods.
-
A.
Introduction to Symplectic Topology
Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
-
B.
Fourier restriction theory
Fourier restriction theory is a branch of harmonic analysis that studies when and how the Fourier transform of a function can be meaningfully restricted to lower-dimensional subsets such as curves or surfaces.
-
C.
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
-
D.
McDuff–Salamon theory of J-holomorphic curves
The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
-
E.
Kähler geometry
Kähler geometry is a branch of differential geometry studying complex manifolds equipped with a compatible symplectic form and Riemannian metric, leading to rich interactions between complex, symplectic, and Riemannian geometry.
- 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_69d6aa8769b4819082bfe5e61b9017f0 |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d770a062f481908beb76c6dbaeb6a6 |
completed | April 9, 2026, 9:25 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e2175711d4819088f93bdf64ba4d3f |
completed | April 17, 2026, 11:19 a.m. |
| NEDg | Description generation | batch_69e21e54e22881908726f088643edfd2 |
completed | April 17, 2026, 11:49 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e21f1134d0819082fcc735da61d347 |
completed | April 17, 2026, 11:52 a.m. |
Created at: April 8, 2026, 9:23 p.m.