Triple
T736583
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Minkowski inequality |
E14946
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Hölder inequality
Hölder inequality is a fundamental result in mathematical analysis that generalizes the Cauchy–Schwarz inequality and provides bounds for integrals or sums of products in Lᵖ spaces.
|
E87726
|
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: Hölder inequality | Statement: [Minkowski inequality, relatedTo, Hölder inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hölder inequality Context triple: [Minkowski inequality, relatedTo, Hölder 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.
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.
-
D.
Cameron–Martin theorem
The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
-
E.
Radon–Nikodym derivative
The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure 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: Hölder inequality Triple: [Minkowski inequality, relatedTo, Hölder inequality]
Generated description
Hölder inequality is a fundamental result in mathematical analysis that generalizes the Cauchy–Schwarz inequality and provides bounds for integrals or sums of products in Lᵖ spaces.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hölder inequality Target entity description: Hölder inequality is a fundamental result in mathematical analysis that generalizes the Cauchy–Schwarz inequality and provides bounds for integrals or sums of products in Lᵖ spaces.
-
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.
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.
-
D.
Cameron–Martin theorem
The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
-
E.
Radon–Nikodym derivative
The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure 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_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.