Triple

T4092353
Position Surface form Disambiguated ID Type / Status
Subject Khinchin–Kahane type inequalities E87730 entity
Predicate hasVariant P455 FINISHED
Object noncommutative Khinchin–Kahane inequalities E87730 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: noncommutative Khinchin–Kahane inequalities | Statement: [Khinchin–Kahane type inequalities, hasVariant, noncommutative Khinchin–Kahane inequalities]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: noncommutative Khinchin–Kahane inequalities
Context triple: [Khinchin–Kahane type inequalities, hasVariant, noncommutative Khinchin–Kahane inequalities]
  • A. Khinchin–Kahane type inequalities chosen
    Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
  • B. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • C. Khinchin's representation theorem
    Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
  • D. Khinchin's law of the iterated logarithm
    Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
  • E. Connes embedding problem
    The Connes embedding problem is a central open question in operator algebras and quantum theory that asks whether every separable II₁ factor can be approximated in a specific way by finite-dimensional matrix algebras.
  • 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_69aed94425148190be337845d56fac22 completed March 9, 2026, 2:29 p.m.
NER Named-entity recognition batch_69aefcae22a081908af65a960306b78c completed March 9, 2026, 5 p.m.
NED1 Entity disambiguation (via context triple) batch_69b56b6cfb288190ac08c3a37327ac9a completed March 14, 2026, 2:06 p.m.
Created at: March 9, 2026, 3:40 p.m.