Triple
T18495191
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hardy inequality |
E451926
|
entity |
| Predicate | hasVariant |
P455
|
FINISHED |
| Object | Hardy inequality on R^n |
—
|
NE NERFINISHED |
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: Hardy inequality on R^n | Statement: [Hardy inequality, hasVariant, Hardy inequality on R^n]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hardy inequality on R^n Context triple: [Hardy inequality, hasVariant, Hardy inequality on R^n]
-
A.
Hardy inequality
chosen
The Hardy inequality is a fundamental result in mathematical analysis that provides bounds on integrals or sums involving a function and its distance from a point, with important applications in functional analysis and partial differential equations.
-
B.
Caffarelli–Kohn–Nirenberg inequalities
The Caffarelli–Kohn–Nirenberg inequalities are a family of weighted interpolation inequalities in analysis that generalize classical Sobolev and Hardy inequalities and play a key role in the study of partial differential equations and regularity theory.
-
C.
Lieb–Thirring inequality
The Lieb–Thirring inequality is a fundamental result in mathematical physics and analysis that provides bounds on sums of negative eigenvalues of Schrödinger operators, with deep applications to quantum mechanics and stability of matter.
-
D.
Morawetz inequalities
Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
-
E.
Sobolev inequality
The Sobolev inequality is a fundamental result in functional analysis and partial differential equations that bounds the size of a function in certain Lebesgue spaces by the size of its derivatives, enabling key embedding and regularity properties.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69d8d3855d50819097fc8561b0299dd9 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e532bfeef4819096b2fa28abb662b9 |
completed | April 19, 2026, 7:53 p.m. |
Created at: April 10, 2026, 11:35 a.m.