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.