Triple
T14314178
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bernstein inequalities |
E354909
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Markov brothers' inequalities
Markov brothers' inequalities are classical results in approximation theory that provide upper bounds on the derivatives of polynomials in terms of their degree and maximum absolute value on an interval.
|
E1093942
|
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: Markov brothers' inequalities | Statement: [Bernstein inequalities, relatedTo, Markov brothers' inequalities]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Markov brothers' inequalities Context triple: [Bernstein inequalities, relatedTo, Markov brothers' inequalities]
-
A.
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.
-
B.
Bernstein polynomials
Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
-
C.
Inequalities for analytic functions
"Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
-
D.
Maclaurin’s inequality in symmetric means
Maclaurin’s inequality in symmetric means is a classical result in mathematical analysis that relates and bounds the sequence of elementary symmetric means of a set of nonnegative real numbers, showing they form a decreasing sequence.
-
E.
Meyer inequalities
Meyer inequalities are fundamental estimates in Malliavin calculus that relate Sobolev-type norms of random variables to norms involving iterated Malliavin derivatives, playing a key role in regularity and integrability results on Wiener space.
- 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: Markov brothers' inequalities Triple: [Bernstein inequalities, relatedTo, Markov brothers' inequalities]
Generated description
Markov brothers' inequalities are classical results in approximation theory that provide upper bounds on the derivatives of polynomials in terms of their degree and maximum absolute value on an interval.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Markov brothers' inequalities Target entity description: Markov brothers' inequalities are classical results in approximation theory that provide upper bounds on the derivatives of polynomials in terms of their degree and maximum absolute value on an interval.
-
A.
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.
-
B.
Bernstein polynomials
Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
-
C.
Inequalities for analytic functions
"Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
-
D.
Maclaurin’s inequality in symmetric means
Maclaurin’s inequality in symmetric means is a classical result in mathematical analysis that relates and bounds the sequence of elementary symmetric means of a set of nonnegative real numbers, showing they form a decreasing sequence.
-
E.
Meyer inequalities
Meyer inequalities are fundamental estimates in Malliavin calculus that relate Sobolev-type norms of random variables to norms involving iterated Malliavin derivatives, playing a key role in regularity and integrability results on Wiener space.
- 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_69d8278ed42c8190b9f882dcce611347 |
completed | April 9, 2026, 10:26 p.m. |
| NER | Named-entity recognition | batch_69de85b49e5481909b9ffab2d922e284 |
completed | April 14, 2026, 6:21 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd4687c6bc819088452892128c420e |
completed | May 8, 2026, 2:12 a.m. |
| NEDg | Description generation | batch_69fd47e2b8d481909ed8274a96615b36 |
completed | May 8, 2026, 2:18 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69fd4879b2688190ac208545ae226c93 |
completed | May 8, 2026, 2:20 a.m. |
Created at: April 10, 2026, 1:12 a.m.