Triple
T12282685
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Malliavin calculus |
E292751
|
entity |
| Predicate | keyConcept |
P531
|
FINISHED |
| Object |
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.
|
E973156
|
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: Meyer inequalities | Statement: [Malliavin calculus, keyConcept, Meyer inequalities]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Meyer inequalities Context triple: [Malliavin calculus, keyConcept, Meyer inequalities]
-
A.
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.
-
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.
Weyl inequalities
Weyl inequalities are fundamental results in linear algebra that bound the eigenvalues of sums of Hermitian (or symmetric) matrices in terms of the eigenvalues of the individual matrices.
-
D.
Korn inequality
Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
-
E.
Chebyshev’s sum inequality
Chebyshev’s sum inequality is a mathematical inequality that provides bounds on the sum of products of similarly ordered sequences, widely used in analysis and probability theory.
- 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: Meyer inequalities Triple: [Malliavin calculus, keyConcept, Meyer inequalities]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Meyer inequalities Target entity description: 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.
-
A.
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.
-
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.
Weyl inequalities
Weyl inequalities are fundamental results in linear algebra that bound the eigenvalues of sums of Hermitian (or symmetric) matrices in terms of the eigenvalues of the individual matrices.
-
D.
Korn inequality
Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
-
E.
Chebyshev’s sum inequality
Chebyshev’s sum inequality is a mathematical inequality that provides bounds on the sum of products of similarly ordered sequences, widely used in analysis and probability theory.
- 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_69d6ab690ad081908c0ed3870ec82d53 |
completed | April 8, 2026, 7:24 p.m. |
| NER | Named-entity recognition | batch_69d91cf2b09c81908a11581d33f65be0 |
completed | April 10, 2026, 3:53 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f61e70dec8819098199fbb54d888c1 |
completed | May 2, 2026, 3:55 p.m. |
| NEDg | Description generation | batch_69f61f5bc1fc8190af9d74acc307ebe1 |
completed | May 2, 2026, 3:59 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69f62041f2408190ad320fec5283abdd |
completed | May 2, 2026, 4:03 p.m. |
Created at: April 8, 2026, 9:52 p.m.