Triple

T11961360
Position Surface form Disambiguated ID Type / Status
Subject Fubini's theorem E284675 entity
Predicate hasVersion P455 FINISHED
Object Fubini's theorem for Bochner integrals E284675 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: Fubini's theorem for Bochner integrals | Statement: [Fubini's theorem, hasVersion, Fubini's theorem for Bochner integrals]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fubini's theorem for Bochner integrals
Context triple: [Fubini's theorem, hasVersion, Fubini's theorem for Bochner integrals]
  • A. Bochner integral
    The Bochner integral is a generalization of the Lebesgue integral to functions taking values in Banach spaces, widely used in functional analysis and probability theory.
  • B. Fubini's theorem chosen
    Fubini's theorem is a fundamental result in measure theory that allows the evaluation of double integrals as iterated integrals under suitable integrability conditions.
  • C. Bochner theorem on characteristic functions
    The Bochner theorem on characteristic functions is a fundamental result in probability theory and harmonic analysis that characterizes which functions are Fourier transforms of probability measures by requiring them to be positive-definite, continuous, and normalized at zero.
  • D. Bochner–Riesz means
    Bochner–Riesz means are a family of summability methods in harmonic analysis used to improve the convergence of Fourier series and Fourier integrals by smoothing their partial sums.
  • E. Leçons d’analyse fonctionnelle
    Leçons d’analyse fonctionnelle is a foundational textbook in functional analysis that helped shape the modern theory of linear operators and Banach and Hilbert spaces.
  • 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_69d6ab2eaeb881909f7914758f859413 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9037848f481908276716675464464 completed April 10, 2026, 2:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69f4592fa9a48190a0450e3d0c57c4d3 completed May 1, 2026, 7:41 a.m.
Created at: April 8, 2026, 9:45 p.m.