Triple
T14637270
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Renato Caccioppoli |
E343638
|
entity |
| Predicate | hasNotableConcept |
P531
|
FINISHED |
| Object | Caccioppoli inequality |
E1109989
|
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: Caccioppoli inequality | Statement: [Renato Caccioppoli, hasNotableConcept, Caccioppoli inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Caccioppoli inequality Context triple: [Renato Caccioppoli, hasNotableConcept, Caccioppoli inequality]
-
A.
Caccioppoli inequality
chosen
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.
-
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.
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.
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.
-
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_69d822dffc3c8190aa173b90761bffda |
completed | April 9, 2026, 10:06 p.m. |
| NER | Named-entity recognition | batch_69deb4aca6448190adf1042dfbfef716 |
completed | April 14, 2026, 9:42 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fdd5d2059081908150b6534aebb32f |
completed | May 8, 2026, 12:23 p.m. |
Created at: April 10, 2026, 1:26 a.m.