Triple

T736603
Position Surface form Disambiguated ID Type / Status
Subject Minkowski inequality E14946 entity
Predicate isSpecialCaseOf P2372 FINISHED
Object Khinchin–Kahane type inequalities
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.
E87730 NE FINISHED

How this triple was built (4 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: Khinchin–Kahane type inequalities | Statement: [Minkowski inequality, isSpecialCaseOf, Khinchin–Kahane type inequalities]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Khinchin–Kahane type inequalities
Context triple: [Minkowski inequality, isSpecialCaseOf, Khinchin–Kahane type inequalities]
  • A. Berry–Esseen theorem
    The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
  • B. Minkowski inequality
    The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
  • C. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • D. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • E. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Khinchin–Kahane type inequalities
Triple: [Minkowski inequality, isSpecialCaseOf, Khinchin–Kahane type inequalities]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Khinchin–Kahane type inequalities
Target entity description: 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.
  • A. Berry–Esseen theorem
    The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
  • B. Minkowski inequality
    The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
  • C. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • D. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • E. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • F. None of above. chosen

Provenance (5 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_69a4934d9930819099eed80096b0597d completed March 1, 2026, 7:28 p.m.
NER Named-entity recognition batch_69a4a5da30b88190afbd12ae6109cc1b completed March 1, 2026, 8:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69a64a618c248190ab1bcecba04d3da8 completed March 3, 2026, 2:41 a.m.
NEDg Description generation batch_69a64b4c8bb88190aa413a4bed256129 completed March 3, 2026, 2:45 a.m.
NED2 Entity disambiguation (via description) batch_69a64beaafa0819099b02cca0f6c79b7 completed March 3, 2026, 2:48 a.m.
Created at: March 1, 2026, 7:37 p.m.