Triple
T17020220
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Sobolev spaces |
E412927
|
entity |
| Predicate | relatedTheorem |
P49212
|
FINISHED |
| Object | Gagliardo–Nirenberg interpolation inequality |
E588689
|
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: Gagliardo–Nirenberg interpolation inequality | Statement: [Sobolev spaces, relatedTheorem, Gagliardo–Nirenberg interpolation inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Gagliardo–Nirenberg interpolation inequality Context triple: [Sobolev spaces, relatedTheorem, Gagliardo–Nirenberg interpolation inequality]
-
A.
Gagliardo–Nirenberg interpolation inequalities
chosen
The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
-
B.
John–Nirenberg inequality
The John–Nirenberg inequality is a fundamental result in harmonic analysis that characterizes functions of bounded mean oscillation (BMO) by showing their oscillations have exponentially decaying distribution.
-
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.
Fefferman–Phong inequality
The Fefferman–Phong inequality is a fundamental result in harmonic analysis and partial differential equations that provides weighted \(L^2\) estimates controlling functions by their gradients and associated potentials.
-
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_69d886cc4170819093deddc7b8b4b6a7 |
completed | April 10, 2026, 5:12 a.m. |
| NER | Named-entity recognition | batch_69e3d482c3a0819099e6ea4acb0a08ee |
completed | April 18, 2026, 6:59 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a011b4f9dfc819085639edb5cda1cca |
completed | May 10, 2026, 11:57 p.m. |
Created at: April 10, 2026, 5:33 a.m.