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.