Triple
T373793
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bernhard Riemann |
E8325
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Über die Hypothesen, welche der Geometrie zu Grunde liegen
"Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
|
E47356
|
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 Hypothesen, welche der Geometrie zu Grunde liegen | Statement: [Bernhard Riemann, notableWork, Über die Hypothesen, welche der Geometrie zu Grunde liegen]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Über die Hypothesen, welche der Geometrie zu Grunde liegen Context triple: [Bernhard Riemann, notableWork, Über die Hypothesen, welche der Geometrie zu Grunde liegen]
-
A.
Grundlagen der Geometrie
Grundlagen der Geometrie is David Hilbert’s foundational 1899 treatise that rigorously axiomatizes Euclidean geometry and helped shape modern mathematical logic and the axiomatic method.
-
B.
Theorema Egregium
Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
-
C.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
-
D.
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.
-
E.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set 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: Über die Hypothesen, welche der Geometrie zu Grunde liegen Triple: [Bernhard Riemann, notableWork, Über die Hypothesen, welche der Geometrie zu Grunde liegen]
Generated description
"Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Über die Hypothesen, welche der Geometrie zu Grunde liegen Target entity description: "Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
-
A.
Grundlagen der Geometrie
Grundlagen der Geometrie is David Hilbert’s foundational 1899 treatise that rigorously axiomatizes Euclidean geometry and helped shape modern mathematical logic and the axiomatic method.
-
B.
Theorema Egregium
Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
-
C.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
-
D.
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.
-
E.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
- 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.