Triple
T9747021
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Alberto Calderón |
E236336
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object |
Calderón transference principle
The Calderón transference principle is a fundamental result in harmonic analysis that allows boundedness properties of operators on one group (often the real line or integers) to be transferred to analogous operators on more general groups or measure spaces.
|
E817948
|
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 transference principle | Statement: [Alberto Calderón, notableFor, Calderón transference principle]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Calderón transference principle Context triple: [Alberto Calderón, notableFor, Calderón transference principle]
-
A.
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.
-
B.
Bourgain–Tzafriri restricted invertibility principle
The Bourgain–Tzafriri restricted invertibility principle is a fundamental result in functional analysis and operator theory that guarantees the existence of large, well-invertible submatrices within certain classes of linear operators.
-
C.
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.
-
D.
Monge–Ampère equation
The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
-
E.
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.
- 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 transference principle Triple: [Alberto Calderón, notableFor, Calderón transference principle]
Generated description
The Calderón transference principle is a fundamental result in harmonic analysis that allows boundedness properties of operators on one group (often the real line or integers) to be transferred to analogous operators on more general groups or measure spaces.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Calderón transference principle Target entity description: The Calderón transference principle is a fundamental result in harmonic analysis that allows boundedness properties of operators on one group (often the real line or integers) to be transferred to analogous operators on more general groups or measure spaces.
-
A.
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.
-
B.
Bourgain–Tzafriri restricted invertibility principle
The Bourgain–Tzafriri restricted invertibility principle is a fundamental result in functional analysis and operator theory that guarantees the existence of large, well-invertible submatrices within certain classes of linear operators.
-
C.
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.
-
D.
Monge–Ampère equation
The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
-
E.
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.
- 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.