Triple
T13893988
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hadamard matrix |
E334040
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Hadamard inequality |
E334041
|
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: Hadamard inequality | Statement: [Hadamard matrix, relatedTo, Hadamard inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hadamard inequality Context triple: [Hadamard matrix, relatedTo, Hadamard inequality]
-
A.
Hadamard inequality
chosen
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.
-
B.
Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality is a fundamental result in linear algebra and analysis that bounds the inner product of two vectors by the product of their magnitudes, underpinning many concepts in geometry, probability, and functional analysis.
-
C.
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.
-
D.
Weyl inequalities
Weyl inequalities are fundamental results in linear algebra that bound the eigenvalues of sums of Hermitian (or symmetric) matrices in terms of the eigenvalues of the individual matrices.
-
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_69d81c5dd2d48190b7a5fc1e009de936 |
completed | April 9, 2026, 9:38 p.m. |
| NER | Named-entity recognition | batch_69de23a741908190bdf46d76c5f1411a |
completed | April 14, 2026, 11:23 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f7c71ca8a881908ac02687fbfe62fb |
completed | May 3, 2026, 10:07 p.m. |
Created at: April 9, 2026, 10:15 p.m.