Triple

T11961357
Position Surface form Disambiguated ID Type / Status
Subject Fubini's theorem E284675 entity
Predicate comparedWith P278 FINISHED
Object Tonelli's theorem for nonnegative functions E284676 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: Tonelli's theorem for nonnegative functions | Statement: [Fubini's theorem, comparedWith, Tonelli's theorem for nonnegative functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Tonelli's theorem for nonnegative functions
Context triple: [Fubini's theorem, comparedWith, Tonelli's theorem for nonnegative functions]
  • A. Tonelli's theorem chosen
    Tonelli's theorem is a fundamental result in measure theory that justifies interchanging the order of integration for non-negative measurable functions in iterated Lebesgue integrals.
  • B. Carathéodory’s extension theorem
    Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
  • C. Kolmogorov zero–one law
    The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
  • D. Doob’s maximal inequalities
    Doob’s maximal inequalities are fundamental results in probability theory that provide bounds on the maximum value of a martingale or submartingale in terms of its expected terminal value, playing a key role in convergence and limit theorems.
  • 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_69f48a83c2448190bb40c199afef2ec2 completed May 1, 2026, 11:12 a.m.
Created at: April 8, 2026, 9:45 p.m.