Triple

T13614701
Position Surface form Disambiguated ID Type / Status
Subject Singular Integrals and Differentiability Properties of Functions E325281 entity
Predicate topic P261 FINISHED
Object Littlewood–Paley theory E412933 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: Littlewood–Paley theory | Statement: [Singular Integrals and Differentiability Properties of Functions, topic, Littlewood–Paley theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Littlewood–Paley theory
Context triple: [Singular Integrals and Differentiability Properties of Functions, topic, Littlewood–Paley theory]
  • A. Littlewood–Paley theory chosen
    Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
  • B. 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.
  • 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. 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.
  • E. 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.
  • 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_69d8076aae28819092cf636190ee5529 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69dbb0ad0a7c81909c7972187202db96 completed April 12, 2026, 2:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69f77f9cbc388190972e949324144d2f completed May 3, 2026, 5:02 p.m.
Created at: April 9, 2026, 9:50 p.m.