Triple
T373791
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bernhard Riemann |
E8325
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
|
E47354
|
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: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe | Statement: [Bernhard Riemann, notableWork, Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe Context triple: [Bernhard Riemann, notableWork, Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe]
-
A.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
B.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
-
C.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
-
D.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
E.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
- 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: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe Triple: [Bernhard Riemann, notableWork, Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe]
Generated description
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe Target entity description: Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
-
A.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
B.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
-
C.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
-
D.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
E.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
- 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_69a2e7f2ec648190b42bc7db424f8109 |
completed | Feb. 28, 2026, 1:04 p.m. |
| NER | Named-entity recognition | batch_69a2ec13b9b48190b294d998c6720132 |
completed | Feb. 28, 2026, 1:22 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69a3f0a9608481908bee4d83768e6497 |
completed | March 1, 2026, 7:54 a.m. |
| NEDg | Description generation | batch_69a3f131d1f88190ac131204c5402687 |
completed | March 1, 2026, 7:56 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69a3f202f308819098affb41d502d5fb |
completed | March 1, 2026, 8 a.m. |
Created at: Feb. 28, 2026, 1:08 p.m.