Triple
T9747022
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Alberto Calderón |
E236336
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object |
Calderón interpolation theorem
The Calderón interpolation theorem is a fundamental result in functional analysis that provides a powerful method for constructing intermediate spaces and extending bounded linear operators between them.
|
E817949
|
NE FINISHED |
How this triple was built (4 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: Calderón interpolation theorem | Statement: [Alberto Calderón, notableFor, Calderón interpolation theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Calderón interpolation theorem Context triple: [Alberto Calderón, notableFor, Calderón interpolation theorem]
-
A.
Riesz–Thorin interpolation theorem
The Riesz–Thorin interpolation theorem is a fundamental result in functional analysis that provides bounds for linear operators between Lᵖ spaces by interpolating their behavior between two known endpoint estimates.
-
B.
Gagliardo–Nirenberg interpolation inequalities
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.
-
C.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
D.
Calderón–Zygmund theory
Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
-
E.
Nevanlinna–Pick interpolation
Nevanlinna–Pick interpolation is a classical problem in complex analysis and operator theory that seeks analytic functions, typically bounded by one in the unit disk, which match prescribed values at given points.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Calderón interpolation theorem Triple: [Alberto Calderón, notableFor, Calderón interpolation theorem]
Generated description
The Calderón interpolation theorem is a fundamental result in functional analysis that provides a powerful method for constructing intermediate spaces and extending bounded linear operators between them.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Calderón interpolation theorem Target entity description: The Calderón interpolation theorem is a fundamental result in functional analysis that provides a powerful method for constructing intermediate spaces and extending bounded linear operators between them.
-
A.
Riesz–Thorin interpolation theorem
The Riesz–Thorin interpolation theorem is a fundamental result in functional analysis that provides bounds for linear operators between Lᵖ spaces by interpolating their behavior between two known endpoint estimates.
-
B.
Gagliardo–Nirenberg interpolation inequalities
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.
-
C.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
D.
Calderón–Zygmund theory
Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
-
E.
Nevanlinna–Pick interpolation
Nevanlinna–Pick interpolation is a classical problem in complex analysis and operator theory that seeks analytic functions, typically bounded by one in the unit disk, which match prescribed values at given points.
- F. None of above. chosen
Provenance (5 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_69ca84d3e24481908a476e2231123cf9 |
completed | March 30, 2026, 2:12 p.m. |
| NER | Named-entity recognition | batch_69cd9f677830819096d388b9c798ecd5 |
completed | April 1, 2026, 10:42 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d1b00d76488190af68cba694dc329c |
completed | April 5, 2026, 12:42 a.m. |
| NEDg | Description generation | batch_69d1b0f7a68481909de080dd78f883a8 |
completed | April 5, 2026, 12:46 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69d1b17bd97c8190b77815db5a6a70d9 |
completed | April 5, 2026, 12:49 a.m. |
Created at: March 30, 2026, 8:23 p.m.