Triple

T9747019
Position Surface form Disambiguated ID Type / Status
Subject Alberto Calderón E236336 entity
Predicate notableFor P22 FINISHED
Object Calderón–Zygmund decomposition E544152 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: Calderón–Zygmund decomposition | Statement: [Alberto Calderón, notableFor, Calderón–Zygmund decomposition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Calderón–Zygmund decomposition
Context triple: [Alberto Calderón, notableFor, Calderón–Zygmund decomposition]
  • A. Calderón–Zygmund theory chosen
    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. Littlewood–Paley theory
    Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
  • C. Three regularity results in harmonic analysis
    "Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
  • D. Riesz transforms
    Riesz transforms are fundamental singular integral operators in harmonic analysis that generalize the Hilbert transform to higher dimensions and play a key role in studying function spaces and partial differential equations.
  • E. Bochner–Riesz means
    Bochner–Riesz means are a family of summability methods in harmonic analysis used to improve the convergence of Fourier series and Fourier integrals by smoothing their partial sums.
  • 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_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.
Created at: March 30, 2026, 8:23 p.m.