Triple

T15502565
Position Surface form Disambiguated ID Type / Status
Subject Khinchin's representation theorem E378996 entity
Predicate isRelatedTo P37 FINISHED
Object Bochner's theorem E613407 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: Bochner's theorem | Statement: [Khinchin's representation theorem, isRelatedTo, Bochner's theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Bochner's theorem
Context triple: [Khinchin's representation theorem, isRelatedTo, Bochner's theorem]
  • A. Bochner theorem on characteristic functions chosen
    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.
  • B. Paley–Wiener theorem
    The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
  • C. Wiener–Khinchin theorem
    The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the Fourier transform.
  • D. Cramér–Wold theorem
    The Cramér–Wold theorem is a fundamental result in probability theory stating that a multivariate distribution is uniquely determined by the distributions of all its one-dimensional linear projections.
  • E. 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.
  • 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_69d85cd53a7c819080f5b9042c4c199e completed April 10, 2026, 2:13 a.m.
NER Named-entity recognition batch_69e03fcc5bb88190b8a9a81419a9a38b completed April 16, 2026, 1:47 a.m.
NED1 Entity disambiguation (via context triple) batch_69ff3669f908819087162b1b8a4e4320 completed May 9, 2026, 1:28 p.m.
Created at: April 10, 2026, 3:54 a.m.