Triple
T23142544
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | graph Laplacian |
E577498
|
entity |
| Predicate | centralConceptIn |
P533
|
FINISHED |
| Object | spectral graph theory |
—
|
NE NERFINISHED |
How this triple was built (2 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: [graph Laplacian, centralConceptIn, spectral graph theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: spectral graph theory Context triple: [graph Laplacian, centralConceptIn, spectral graph theory]
-
A.
Spectral Graph Theory
chosen
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
spectral geometry
Spectral geometry is a field of mathematics that studies how the geometric and topological properties of spaces are reflected in the spectra of associated differential operators.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69e245f8e6248190ba3d58e068b4dccb |
completed | April 17, 2026, 2:38 p.m. |
| NER | Named-entity recognition | batch_69f18ecb72fc8190a24e8f5756217a36 |
completed | April 29, 2026, 4:53 a.m. |
Created at: April 17, 2026, 4 p.m.