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.