Triple
T17020130
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Karamata's inequality |
E412925
|
entity |
| Predicate | hasAlternativeName |
P39
|
FINISHED |
| Object | Karamata majorization inequality |
E412925
|
NE FINISHED |
How this triple was built (2 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: Karamata majorization inequality | Statement: [Karamata's inequality, hasAlternativeName, Karamata majorization inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Karamata majorization inequality Context triple: [Karamata's inequality, hasAlternativeName, Karamata majorization inequality]
-
A.
Karamata's inequality
chosen
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d886cc4170819093deddc7b8b4b6a7 |
completed | April 10, 2026, 5:12 a.m. |
| NER | Named-entity recognition | batch_69e3d482c3a0819099e6ea4acb0a08ee |
completed | April 18, 2026, 6:59 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a011b4f9dfc819085639edb5cda1cca |
completed | May 10, 2026, 11:57 p.m. |
Created at: April 10, 2026, 5:33 a.m.