Triple

T11961904
Position Surface form Disambiguated ID Type / Status
Subject Johann Radon E284687 entity
Predicate hasConceptNamedAfter P3325 FINISHED
Object Radon integral
The Radon integral is a mathematical construction in measure theory and integral geometry that generalizes classical integration by integrating functions over families of sets, such as lines or hyperplanes, rather than just over intervals or regions.
E956299 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: Radon integral | Statement: [Johann Radon, hasConceptNamedAfter, Radon integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Radon integral
Context triple: [Johann Radon, hasConceptNamedAfter, Radon integral]
  • A. Radon measure
    A Radon measure is a type of measure on a topological space that is locally finite and inner regular, playing a central role in modern measure theory and integration.
  • B. Radon transform
    The Radon transform is an integral transform that maps a function to its line integrals over hyperplanes, forming the mathematical foundation of computed tomography and various inverse problems in imaging.
  • C. Poisson integral
    The Poisson integral is a fundamental formula in harmonic analysis that reconstructs harmonic functions inside a disk (or half-plane) from their boundary values using the Poisson kernel.
  • D. Radon space
    A Radon space is a topological space in which every finite Borel measure is inner regular, meaning the measure of any Borel set can be approximated from within by compact subsets.
  • E. Radon–Nikodym derivative
    The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure theory.
  • 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: Radon integral
Triple: [Johann Radon, hasConceptNamedAfter, Radon integral]
Generated description
The Radon integral is a mathematical construction in measure theory and integral geometry that generalizes classical integration by integrating functions over families of sets, such as lines or hyperplanes, rather than just over intervals or regions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Radon integral
Target entity description: The Radon integral is a mathematical construction in measure theory and integral geometry that generalizes classical integration by integrating functions over families of sets, such as lines or hyperplanes, rather than just over intervals or regions.
  • A. Radon measure
    A Radon measure is a type of measure on a topological space that is locally finite and inner regular, playing a central role in modern measure theory and integration.
  • B. Radon transform chosen
    The Radon transform is an integral transform that maps a function to its line integrals over hyperplanes, forming the mathematical foundation of computed tomography and various inverse problems in imaging.
  • C. Poisson integral
    The Poisson integral is a fundamental formula in harmonic analysis that reconstructs harmonic functions inside a disk (or half-plane) from their boundary values using the Poisson kernel.
  • D. Radon space
    A Radon space is a topological space in which every finite Borel measure is inner regular, meaning the measure of any Borel set can be approximated from within by compact subsets.
  • E. Radon–Nikodym derivative
    The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure theory.
  • F. None of above.

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_69d6ab2eaeb881909f7914758f859413 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9037848f481908276716675464464 completed April 10, 2026, 2:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69f471d625c88190baed4ea08853988a completed May 1, 2026, 9:26 a.m.
NEDg Description generation batch_69f47b7ac4048190ae09f18f1a90338f completed May 1, 2026, 10:07 a.m.
NED2 Entity disambiguation (via description) batch_69f47db91f38819092b7b5c5e2bb489b completed May 1, 2026, 10:17 a.m.
Created at: April 8, 2026, 9:45 p.m.