Triple

T12597233
Position Surface form Disambiguated ID Type / Status
Subject Colin Maclaurin E300763 entity
Predicate knownFor P22 FINISHED
Object 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.
E992326 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: Maclaurin’s inequality in symmetric means | Statement: [Colin Maclaurin, knownFor, Maclaurin’s inequality in symmetric means]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Maclaurin’s inequality in symmetric means
Context triple: [Colin Maclaurin, knownFor, Maclaurin’s inequality in symmetric means]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Hadamard inequality
    The Hadamard inequality is a fundamental result in linear algebra and analysis that bounds the absolute value of a determinant by the product of the Euclidean norms of its row or column vectors.
  • E. Riesz rearrangement inequality
    The Riesz rearrangement inequality is a fundamental result in mathematical analysis that provides an optimal bound for integrals of products of functions in terms of their symmetric decreasing rearrangements.
  • 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: Maclaurin’s inequality in symmetric means
Triple: [Colin Maclaurin, knownFor, Maclaurin’s inequality in symmetric means]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Maclaurin’s inequality in symmetric means
Target entity description: 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.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Hadamard inequality
    The Hadamard inequality is a fundamental result in linear algebra and analysis that bounds the absolute value of a determinant by the product of the Euclidean norms of its row or column vectors.
  • E. Riesz rearrangement inequality
    The Riesz rearrangement inequality is a fundamental result in mathematical analysis that provides an optimal bound for integrals of products of functions in terms of their symmetric decreasing rearrangements.
  • 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_69d7bdea2ca881908f379526c13b1145 completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d954cf33b88190bff339fcd3142cc8 completed April 10, 2026, 7:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69f65ec75fc08190aa13cbb0161eb35c completed May 2, 2026, 8:29 p.m.
NEDg Description generation batch_69f6605bca10819086966e1574c31318 completed May 2, 2026, 8:36 p.m.
NED2 Entity disambiguation (via description) batch_69f6617997188190bfce14c54619af7f completed May 2, 2026, 8:41 p.m.
Created at: April 9, 2026, 5:08 p.m.