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.