Triple

T736584
Position Surface form Disambiguated ID Type / Status
Subject Minkowski inequality E14946 entity
Predicate relatedTo P37 FINISHED
Object Jensen inequality
Jensen's inequality is a fundamental result in convex analysis and probability theory that relates the value of a convex (or concave) function of an expectation to the expectation of the function, providing bounds that underlie many other inequalities and convergence results.
E87727 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: Jensen inequality | Statement: [Minkowski inequality, relatedTo, Jensen inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Jensen inequality
Context triple: [Minkowski inequality, relatedTo, Jensen inequality]
  • A. 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.
  • B. 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.
  • C. Rényi divergence
    Rényi divergence is a family of information-theoretic measures that generalize Kullback–Leibler divergence to quantify the dissimilarity between probability distributions, parameterized by an order α.
  • D. Karush–Kuhn–Tucker conditions
    The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
  • E. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • 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: Jensen inequality
Triple: [Minkowski inequality, relatedTo, Jensen inequality]
Generated description
Jensen's inequality is a fundamental result in convex analysis and probability theory that relates the value of a convex (or concave) function of an expectation to the expectation of the function, providing bounds that underlie many other inequalities and convergence results.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Jensen inequality
Target entity description: Jensen's inequality is a fundamental result in convex analysis and probability theory that relates the value of a convex (or concave) function of an expectation to the expectation of the function, providing bounds that underlie many other inequalities and convergence results.
  • A. 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.
  • B. 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.
  • C. Rényi divergence
    Rényi divergence is a family of information-theoretic measures that generalize Kullback–Leibler divergence to quantify the dissimilarity between probability distributions, parameterized by an order α.
  • D. Karush–Kuhn–Tucker conditions
    The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
  • E. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • 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_69a4934d9930819099eed80096b0597d completed March 1, 2026, 7:28 p.m.
NER Named-entity recognition batch_69a4a5da30b88190afbd12ae6109cc1b completed March 1, 2026, 8:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69a64a618c248190ab1bcecba04d3da8 completed March 3, 2026, 2:41 a.m.
NEDg Description generation batch_69a64b4c8bb88190aa413a4bed256129 completed March 3, 2026, 2:45 a.m.
NED2 Entity disambiguation (via description) batch_69a64beaafa0819099b02cca0f6c79b7 completed March 3, 2026, 2:48 a.m.
Created at: March 1, 2026, 7:37 p.m.