Triple

T4552117
Position Surface form Disambiguated ID Type / Status
Subject Inequalities E120388 entity
Predicate containsTopic P24066 FINISHED
Object Chebyshev inequalities
Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
E451512 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: Chebyshev inequalities | Statement: [Inequalities, containsTopic, Chebyshev inequalities]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Chebyshev inequalities
Context triple: [Inequalities, containsTopic, Chebyshev 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. Bernstein inequalities
    Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
  • C. Cauchy–Schwarz inequality
    The Cauchy–Schwarz inequality is a fundamental result in linear algebra and analysis that bounds the inner product of two vectors by the product of their magnitudes, underpinning many concepts in geometry, probability, and functional analysis.
  • D. 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.
  • E. Karamata's inequality
    Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
  • 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: Chebyshev inequalities
Triple: [Inequalities, containsTopic, Chebyshev inequalities]
Generated description
Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Chebyshev inequalities
Target entity description: Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
  • 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. Bernstein inequalities
    Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
  • C. Cauchy–Schwarz inequality
    The Cauchy–Schwarz inequality is a fundamental result in linear algebra and analysis that bounds the inner product of two vectors by the product of their magnitudes, underpinning many concepts in geometry, probability, and functional analysis.
  • D. 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.
  • E. Karamata's inequality
    Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
  • 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_69bd4636f1648190a701445c2fcd9c17 completed March 20, 2026, 1:05 p.m.
NER Named-entity recognition batch_69bd57f7b9748190af29d02fc77b02e0 completed March 20, 2026, 2:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69bdb95b01b0819094a600752e41aa09 completed March 20, 2026, 9:17 p.m.
NEDg Description generation batch_69bdbdbf73508190b64a78ff9274ee6d completed March 20, 2026, 9:35 p.m.
NED2 Entity disambiguation (via description) batch_69bdbe1bcd8c819094adea59c91c6f5b completed March 20, 2026, 9:37 p.m.
Created at: March 20, 2026, 1:09 p.m.