Triple

T6834241
Position Surface form Disambiguated ID Type / Status
Subject Fan Chung E157409 entity
Predicate notableWork P4 FINISHED
Object 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.
E621125 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: Spectral Graph Theory | Statement: [Fan Chung, notableWork, Spectral Graph Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Spectral Graph Theory
Context triple: [Fan Chung, notableWork, Spectral Graph Theory]
  • A. Laplacian spectrum
    The Laplacian spectrum is the collection of eigenvalues of the Laplace operator on a domain or manifold, encoding how functions vibrate or diffuse over it and serving as a key tool in spectral geometry and mathematical physics.
  • B. Convex Optimization of Graph Laplacian Eigenvalues
    "Convex Optimization of Graph Laplacian Eigenvalues" is a research work by Stephen P. Boyd that develops convex optimization methods to analyze and design graphs via the spectral properties of their Laplacian matrices.
  • C. Graph Algorithms (book)
    "Graph Algorithms" is a foundational textbook by Shimon Even that systematically presents the theory, design, and analysis of algorithms for solving fundamental problems on graphs.
  • D. graph Laplacian
    The graph Laplacian is a matrix representation of a graph that encodes its connectivity and is fundamental in spectral graph theory, clustering, and network analysis.
  • E. Conway's 99-graph problem
    Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
  • 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: Spectral Graph Theory
Triple: [Fan Chung, notableWork, Spectral Graph Theory]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Spectral Graph Theory
Target entity description: 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.
  • A. Laplacian spectrum
    The Laplacian spectrum is the collection of eigenvalues of the Laplace operator on a domain or manifold, encoding how functions vibrate or diffuse over it and serving as a key tool in spectral geometry and mathematical physics.
  • B. Convex Optimization of Graph Laplacian Eigenvalues
    "Convex Optimization of Graph Laplacian Eigenvalues" is a research work by Stephen P. Boyd that develops convex optimization methods to analyze and design graphs via the spectral properties of their Laplacian matrices.
  • C. Graph Algorithms (book)
    "Graph Algorithms" is a foundational textbook by Shimon Even that systematically presents the theory, design, and analysis of algorithms for solving fundamental problems on graphs.
  • D. graph Laplacian
    The graph Laplacian is a matrix representation of a graph that encodes its connectivity and is fundamental in spectral graph theory, clustering, and network analysis.
  • E. Conway's 99-graph problem
    Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
  • 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_69c6882c53608190b99aebef079b23bd completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d67936288190829fedc3729aadd8 completed March 27, 2026, 7:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69c723fd50c88190af005fd58ca0aee6 completed March 28, 2026, 12:42 a.m.
NEDg Description generation batch_69c7247806808190ac60c134cec612c8 completed March 28, 2026, 12:44 a.m.
NED2 Entity disambiguation (via description) batch_69c7253b94f081909e7cee870a12af6b completed March 28, 2026, 12:47 a.m.
Created at: March 27, 2026, 2:18 p.m.