Triple

T5256233
Position Surface form Disambiguated ID Type / Status
Subject Carathéodory’s extension theorem E118705 entity
Predicate instanceOf P0 FINISHED
Object result in measure theory C11644 CONCEPT FINISHED

How this triple was built (1 step)

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.

CD Concept disambiguation gpt-5-mini-2025-08-07 
Target class: result in measure theory
Context triple: [Carathéodory’s extension theorem, instanceOf, result in measure theory]
  • A. measure-theoretic construction chosen
    A measure-theoretic construction is a rigorous method of building mathematical objects—such as measures, integrals, or probability spaces—by specifying σ-algebras, set functions, and limiting processes that satisfy the axioms of measure theory.
  • B. result in real analysis
    In real analysis, a result is a proven mathematical statement—such as a theorem, lemma, proposition, or corollary—that establishes a specific property or relationship about real-valued functions, sequences, sets, or structures on the real numbers.
  • C. result in probability theory
    In probability theory, a result is a formally stated and proven fact—such as a theorem, lemma, or corollary—that describes a property or relationship involving probabilistic concepts like random variables, events, or distributions.
  • D. functional analysis result
    A functional analysis result is a formal conclusion or theorem that characterizes the behavior, structure, or properties of functions and operators on infinite-dimensional spaces, typically within the framework of normed, Banach, or Hilbert spaces.
  • E. result in convex analysis
    In convex analysis, a result is a formally stated and proven fact—such as a theorem, lemma, or proposition—that characterizes properties or relationships of convex sets, convex functions, or related optimization structures.
  • F. None of above.

Provenance (1 batch)

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_69bd446978108190bb5f9c5c23d93f88 completed March 20, 2026, 12:58 p.m.
Created at: March 20, 2026, 1:50 p.m.