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.