Triple

T13614724
Position Surface form Disambiguated ID Type / Status
Subject Singular Integrals and Differentiability Properties of Functions E325281 entity
Predicate topic P261 FINISHED
Object Lebesgue differentiation theorem E451526 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: Lebesgue differentiation theorem | Statement: [Singular Integrals and Differentiability Properties of Functions, topic, Lebesgue differentiation theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lebesgue differentiation theorem
Context triple: [Singular Integrals and Differentiability Properties of Functions, topic, Lebesgue differentiation theorem]
  • A. Lebesgue differentiation theorem chosen
    The Lebesgue differentiation theorem is a fundamental result in real analysis stating that, for an integrable function, the averages over shrinking neighborhoods converge almost everywhere to the function’s pointwise value.
  • B. Lebesgue integration
    Lebesgue integration is a foundational measure-theoretic framework for defining and analyzing integrals, particularly suited to handling limits, convergence, and more general functions than those allowed by Riemann integration.
  • C. 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.
  • D. Denjoy–Young–Saks theorem
    The Denjoy–Young–Saks theorem is a result in real analysis that classifies the possible behaviors of the derivative of a real function at almost every point on the real line.
  • E. Lebesgue measure
    Lebesgue measure is the standard way of assigning a consistent notion of "length," "area," or "volume" to subsets of Euclidean space, forming the foundation of modern measure theory and integration.
  • 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.