Triple
T18495200
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hardy inequality |
E451926
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Sobolev inequality |
E620673
|
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: Sobolev inequality | Statement: [Hardy inequality, relatedTo, Sobolev inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Sobolev inequality Context triple: [Hardy inequality, relatedTo, Sobolev inequality]
-
A.
Sobolev inequality
chosen
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.
-
B.
Poincaré inequality
The Poincaré inequality is a fundamental result in functional analysis and partial differential equations that bounds the average oscillation of a function by the size of its gradient, playing a key role in Sobolev space theory and the study of elliptic problems.
-
C.
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.
-
D.
Friedrichs inequality
Friedrichs inequality is a fundamental result in functional analysis and partial differential equations that provides bounds on the norms of functions in terms of their derivatives, playing a key role in the theory of Sobolev spaces and boundary value problems.
-
E.
Caccioppoli inequality
The Caccioppoli inequality is a fundamental estimate in the theory of partial differential equations that bounds the energy (gradient) of a solution in a smaller region by its values in a larger surrounding region, playing a key role in regularity theory.
- 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.