Triple

T5709650
Position Surface form Disambiguated ID Type / Status
Subject Elias Stein E125871 entity
Predicate notableWork P4 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: [Elias Stein, notableWork, 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: [Elias Stein, notableWork, 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. 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.
  • C. Fefferman–Phong inequality
    The Fefferman–Phong inequality is a fundamental result in harmonic analysis and partial differential equations that provides weighted \(L^2\) estimates controlling functions by their gradients and associated potentials.
  • D. Sobolev spaces
    Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
  • E. Hardy–Littlewood maximal function
    The Hardy–Littlewood maximal function is a fundamental operator in real analysis and harmonic analysis that controls the local averages of a function and plays a key role in differentiation theorems and singular integral theory.
  • 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_69c0082d6fe48190b777fb383769e5c8 completed March 22, 2026, 3:18 p.m.
NER Named-entity recognition batch_69c0248c3dac8190824fca9ddde89665 completed March 22, 2026, 5:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69c05a6f5ac08190b5acbccea756d2de completed March 22, 2026, 9:09 p.m.
Created at: March 22, 2026, 3:46 p.m.