Triple

T21972982
Position Surface form Disambiguated ID Type / Status
Subject Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals E542636 entity
Predicate relatedWork P37 FINISHED
Object Singular Integrals and Differentiability Properties of Functions E325281 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: Singular Integrals and Differentiability Properties of Functions | Statement: [Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, relatedWork, Singular Integrals and Differentiability Properties of Functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Singular Integrals and Differentiability Properties of Functions
Context triple: [Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, relatedWork, Singular Integrals and Differentiability Properties of Functions]
  • A. Singular Integrals and Differentiability Properties of Functions chosen
    "Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
  • B. 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.
  • C. Three regularity results in harmonic analysis
    "Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
  • D. Jessen’s theorem in harmonic analysis
    Jessen’s theorem in harmonic analysis is a result that provides conditions under which certain trigonometric or Fourier series converge almost everywhere, reflecting Børge Jessen’s contributions to the study of convergence phenomena in harmonic analysis.
  • E. Calderón–Zygmund theory
    Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
  • 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_69e0c48070988190909db97667b9a0ac completed April 16, 2026, 11:14 a.m.
NER Named-entity recognition batch_69f124857dcc8190ab474cd8ab9c130a completed April 28, 2026, 9:20 p.m.
NED1 Entity disambiguation (via context triple) batch_6a0a6718c3fc8190bd74e5085e4d3b8b completed May 18, 2026, 1:10 a.m.
Created at: April 16, 2026, 8:02 p.m.