Triple
T18495187
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hardy inequality |
E451926
|
entity |
| Predicate | hasVariant |
P455
|
FINISHED |
| Object | Hardy–Rellich inequality |
E451926
|
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: Hardy–Rellich inequality | Statement: [Hardy inequality, hasVariant, Hardy–Rellich inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hardy–Rellich inequality Context triple: [Hardy inequality, hasVariant, Hardy–Rellich inequality]
-
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.
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.
-
C.
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.
-
D.
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.
-
E.
Korn inequality
Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
- 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_69d8d3855d50819097fc8561b0299dd9 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e532bfeef4819096b2fa28abb662b9 |
completed | April 19, 2026, 7:53 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a04713de2288190aa3cfbce3f817a7e |
completed | May 13, 2026, 12:40 p.m. |
Created at: April 10, 2026, 11:35 a.m.