Triple
T7833351
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lyapunov inequality |
E181627
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Jensen inequality |
E87727
|
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: Jensen inequality | Statement: [Lyapunov inequality, relatedTo, Jensen inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Jensen inequality Context triple: [Lyapunov inequality, relatedTo, Jensen inequality]
-
A.
Jensen inequality
chosen
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.
-
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.
Young's inequality
Young's inequality is a fundamental result in mathematical analysis that provides an upper bound for the product of two nonnegative numbers in terms of their powers, playing a key role in convex analysis and functional inequalities.
-
D.
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.
-
E.
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.
- 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_69ca8284a25c8190a1a20afad30da792 |
completed | March 30, 2026, 2:02 p.m. |
| NER | Named-entity recognition | batch_69cb064a47648190af2ca2b336584a92 |
completed | March 30, 2026, 11:24 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69cb5a9b7bb081909d6aa066ee064093 |
completed | March 31, 2026, 5:24 a.m. |
Created at: March 30, 2026, 4:45 p.m.