Triple

T15918629
Position Surface form Disambiguated ID Type / Status
Subject Szekeres–Lindström theorem E386034 entity
Predicate usedIn P98 FINISHED
Object graph theory
Graph theory is a branch of mathematics that studies the properties and applications of graphs, which model pairwise relationships between objects using vertices and edges.
E1182413 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: graph theory | Statement: [Szekeres–Lindström theorem, usedIn, graph theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: graph theory
Context triple: [Szekeres–Lindström theorem, usedIn, graph theory]
  • A. Introduction to Graph Theory
    Introduction to Graph Theory is a widely used textbook that provides a clear and accessible introduction to the fundamental concepts and techniques of graph theory.
  • B. Graphs and Applications
    Graphs and Applications is a well-known textbook by Richard J. Wilson that introduces graph theory and demonstrates its use in solving practical problems across science, engineering, and computer science.
  • C. Ramsey theory
    Ramsey theory is a branch of combinatorics that studies the conditions under which order or structure must appear within sufficiently large or complex mathematical objects.
  • D. Spectral Graph Theory
    Spectral Graph Theory is a mathematical field that studies graphs through the eigenvalues and eigenvectors of matrices associated with them, such as adjacency and Laplacian matrices, with applications across combinatorics, computer science, and network analysis.
  • E. Cayley graph
    A Cayley graph is a graphical representation of a group where vertices correspond to group elements and edges represent multiplication by chosen generators, widely used in group theory and geometric group 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: graph theory
Triple: [Szekeres–Lindström theorem, usedIn, graph theory]
Generated description
Graph theory is a branch of mathematics that studies the properties and applications of graphs, which model pairwise relationships between objects using vertices and edges.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: graph theory
Target entity description: Graph theory is a branch of mathematics that studies the properties and applications of graphs, which model pairwise relationships between objects using vertices and edges.
  • A. Introduction to Graph Theory
    Introduction to Graph Theory is a widely used textbook that provides a clear and accessible introduction to the fundamental concepts and techniques of graph theory.
  • B. Graphs and Applications
    Graphs and Applications is a well-known textbook by Richard J. Wilson that introduces graph theory and demonstrates its use in solving practical problems across science, engineering, and computer science.
  • C. Ramsey theory
    Ramsey theory is a branch of combinatorics that studies the conditions under which order or structure must appear within sufficiently large or complex mathematical objects.
  • D. Spectral Graph Theory
    Spectral Graph Theory is a mathematical field that studies graphs through the eigenvalues and eigenvectors of matrices associated with them, such as adjacency and Laplacian matrices, with applications across combinatorics, computer science, and network analysis.
  • E. Cayley graph
    A Cayley graph is a graphical representation of a group where vertices correspond to group elements and edges represent multiplication by chosen generators, widely used in group theory and geometric group 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_69d86da686e4819097cbf3b1fc2d881d completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e1567ff9e48190b73cb101fc3f7b2b completed April 16, 2026, 9:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69ffb05d1fb481909b42bea774a15c70 completed May 9, 2026, 10:08 p.m.
NEDg Description generation batch_69ffb0cfac808190b32bb25659603fb4 completed May 9, 2026, 10:10 p.m.
NED2 Entity disambiguation (via description) batch_69ffb15b987c8190ae9c96f15fc55b27 completed May 9, 2026, 10:12 p.m.
Created at: April 10, 2026, 4:52 a.m.