Triple
T373781
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bernhard Riemann |
E8325
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Riemann mapping theorem
The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
|
E47349
|
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: Riemann mapping theorem | Statement: [Bernhard Riemann, knownFor, Riemann mapping theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Riemann mapping theorem Context triple: [Bernhard Riemann, knownFor, Riemann mapping theorem]
-
A.
Brouwer fixed-point theorem
The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
-
B.
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.
-
C.
Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
-
D.
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.
-
E.
Gauss–Bonnet theorem (early form)
The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
- 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: Riemann mapping theorem Triple: [Bernhard Riemann, knownFor, Riemann mapping theorem]
Generated description
The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Riemann mapping theorem Target entity description: The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
-
A.
Brouwer fixed-point theorem
The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
-
B.
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.
-
C.
Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
-
D.
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.
-
E.
Gauss–Bonnet theorem (early form)
The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
- 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.