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.