Triple

T9747017
Position Surface form Disambiguated ID Type / Status
Subject Alberto Calderón E236336 entity
Predicate notableFor P22 FINISHED
Object Calderón reproducing formula
The Calderón reproducing formula is a fundamental result in harmonic analysis that provides an exact reconstruction of functions from their wavelet or frequency decompositions, forming a basis for modern wavelet theory and related analysis.
E817946 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 reproducing formula | Statement: [Alberto Calderón, notableFor, Calderón reproducing formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Calderón reproducing formula
Context triple: [Alberto Calderón, notableFor, Calderón reproducing formula]
  • A. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • B. Kubo formula
    The Kubo formula is a fundamental result in linear response theory that expresses transport coefficients and response functions in terms of equilibrium correlation functions in statistical mechanics and quantum many-body physics.
  • C. Sommerfeld-Watson transform
    The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
  • D. Bochner–Kodaira–Nakano identity
    The Bochner–Kodaira–Nakano identity is a fundamental formula in complex differential geometry relating the Laplacian on differential forms to curvature terms, with key applications to vanishing theorems and Hodge theory.
  • E. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • 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 reproducing formula
Triple: [Alberto Calderón, notableFor, Calderón reproducing formula]
Generated description
The Calderón reproducing formula is a fundamental result in harmonic analysis that provides an exact reconstruction of functions from their wavelet or frequency decompositions, forming a basis for modern wavelet theory and related analysis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Calderón reproducing formula
Target entity description: The Calderón reproducing formula is a fundamental result in harmonic analysis that provides an exact reconstruction of functions from their wavelet or frequency decompositions, forming a basis for modern wavelet theory and related analysis.
  • A. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • B. Kubo formula
    The Kubo formula is a fundamental result in linear response theory that expresses transport coefficients and response functions in terms of equilibrium correlation functions in statistical mechanics and quantum many-body physics.
  • C. Sommerfeld-Watson transform
    The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
  • D. Bochner–Kodaira–Nakano identity
    The Bochner–Kodaira–Nakano identity is a fundamental formula in complex differential geometry relating the Laplacian on differential forms to curvature terms, with key applications to vanishing theorems and Hodge theory.
  • E. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • 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.