Triple

T11961400
Position Surface form Disambiguated ID Type / Status
Subject Tonelli's theorem E284676 entity
Predicate comparedWith P278 FINISHED
Object Fubini's theorem for integrable (not necessarily non‑negative) functions 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 integrable (not necessarily non‑negative) functions | Statement: [Tonelli's theorem, comparedWith, Fubini's theorem for integrable (not necessarily non‑negative) functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fubini's theorem for integrable (not necessarily non‑negative) functions
Context triple: [Tonelli's theorem, comparedWith, Fubini's theorem for integrable (not necessarily non‑negative) functions]
  • A. 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.
  • B. Dirichlet theorem on Fourier series
    The Dirichlet theorem on Fourier series gives conditions under which a periodic function can be represented by a convergent Fourier series, specifying how and where the series converges to the function.
  • C. 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.
  • D. Singular Integrals and Differentiability Properties of Functions
    "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.
  • E. Pisier’s factorization theorems
    Pisier’s factorization theorems are fundamental results in functional analysis and operator theory that provide deep factorization properties for linear and multilinear operators on Banach spaces, extending and refining ideas related to Grothendieck-type inequalities.
  • 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_69f471d625c88190baed4ea08853988a completed May 1, 2026, 9:26 a.m.
Created at: April 8, 2026, 9:45 p.m.