Triple
T4764130
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Seven Bridges of Königsberg problem |
E105766
|
entity |
| Predicate | publishedIn |
P309
|
FINISHED |
| Object |
“Solutio problematis ad geometriam situs pertinentis”
“Solutio problematis ad geometriam situs pertinentis” is Leonhard Euler’s 1736 Latin paper that founded graph theory and topology by solving the Seven Bridges of Königsberg problem.
|
E467733
|
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: “Solutio problematis ad geometriam situs pertinentis” | Statement: [Seven Bridges of Königsberg problem, publishedIn, “Solutio problematis ad geometriam situs pertinentis”]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: “Solutio problematis ad geometriam situs pertinentis” Context triple: [Seven Bridges of Königsberg problem, publishedIn, “Solutio problematis ad geometriam situs pertinentis”]
-
A.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
-
B.
Disquisitiones Generales Circa Superficies Curvas
Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
-
C.
Commentary on the Difficulties of Certain Postulates of Euclid
Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
-
D.
De institutione geometrica
De institutione geometrica is a late antique Latin treatise on geometry that adapts and transmits classical Greek mathematical knowledge within the framework of the quadrivium.
-
E.
The Foundations of Geometry
The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
- 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: “Solutio problematis ad geometriam situs pertinentis” Triple: [Seven Bridges of Königsberg problem, publishedIn, “Solutio problematis ad geometriam situs pertinentis”]
Generated description
“Solutio problematis ad geometriam situs pertinentis” is Leonhard Euler’s 1736 Latin paper that founded graph theory and topology by solving the Seven Bridges of Königsberg problem.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: “Solutio problematis ad geometriam situs pertinentis” Target entity description: “Solutio problematis ad geometriam situs pertinentis” is Leonhard Euler’s 1736 Latin paper that founded graph theory and topology by solving the Seven Bridges of Königsberg problem.
-
A.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
-
B.
Disquisitiones Generales Circa Superficies Curvas
Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
-
C.
Commentary on the Difficulties of Certain Postulates of Euclid
Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
-
D.
De institutione geometrica
De institutione geometrica is a late antique Latin treatise on geometry that adapts and transmits classical Greek mathematical knowledge within the framework of the quadrivium.
-
E.
The Foundations of Geometry
The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
- 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_69bd43f14cac819081c7c69803648211 |
completed | March 20, 2026, 12:56 p.m. |
| NER | Named-entity recognition | batch_69bd6530f0648190b76db9964471cfeb |
completed | March 20, 2026, 3:18 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69be3a87741081909380c51ba4efed92 |
completed | March 21, 2026, 6:28 a.m. |
| NEDg | Description generation | batch_69be3d444b888190b2df7433502604ff |
completed | March 21, 2026, 6:40 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69be3dd31c648190bfdac15fb85cfec9 |
completed | March 21, 2026, 6:42 a.m. |
Created at: March 20, 2026, 1:21 p.m.