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.