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.