Triple
T736585
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Minkowski inequality |
E14946
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Cauchy–Schwarz inequality |
E87726
|
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: Cauchy–Schwarz inequality | Statement: [Minkowski inequality, relatedTo, Cauchy–Schwarz inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cauchy–Schwarz inequality Context triple: [Minkowski inequality, relatedTo, Cauchy–Schwarz 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.
Hölder inequality
chosen
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.
-
C.
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.
-
D.
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.
-
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.
- 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_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_69a654e1d10c8190b69b30cc70add604 |
completed | March 3, 2026, 3:26 a.m. |
Created at: March 1, 2026, 7:37 p.m.