Triple
T4539862
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Stephen P. Boyd |
E107500
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
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.
|
E451069
|
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: Convex Optimization of Graph Laplacian Eigenvalues | Statement: [Stephen P. Boyd, notableWork, Convex Optimization of Graph Laplacian Eigenvalues]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Convex Optimization of Graph Laplacian Eigenvalues Context triple: [Stephen P. Boyd, notableWork, Convex Optimization of Graph Laplacian Eigenvalues]
-
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.
Nonlinear programming
Nonlinear programming is a branch of mathematical optimization focused on finding optimal solutions to problems where the objective function or constraints are nonlinear.
-
C.
Kailath factorization in linear systems
Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
-
D.
The Convexity of Hilltops
"The Convexity of Hilltops" is a seminal geomorphological study by American geologist Grove Karl Gilbert that analyzes the shapes and formation processes of hilltops in relation to erosion and landscape evolution.
-
E.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
- 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: Convex Optimization of Graph Laplacian Eigenvalues Triple: [Stephen P. Boyd, notableWork, Convex Optimization of Graph Laplacian Eigenvalues]
Generated description
"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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Convex Optimization of Graph Laplacian Eigenvalues Target entity description: "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.
-
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.
Nonlinear programming
Nonlinear programming is a branch of mathematical optimization focused on finding optimal solutions to problems where the objective function or constraints are nonlinear.
-
C.
Kailath factorization in linear systems
Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
-
D.
The Convexity of Hilltops
"The Convexity of Hilltops" is a seminal geomorphological study by American geologist Grove Karl Gilbert that analyzes the shapes and formation processes of hilltops in relation to erosion and landscape evolution.
-
E.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
- 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_69bd43f922788190b7edfa294e39b178 |
completed | March 20, 2026, 12:56 p.m. |
| NER | Named-entity recognition | batch_69bd57bb5c0c819092ebb2dd3310f5f8 |
completed | March 20, 2026, 2:20 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bdacfff41481908a5c97ab4fcb9259 |
completed | March 20, 2026, 8:24 p.m. |
| NEDg | Description generation | batch_69bdb32911cc8190a8624d54dad6355e |
completed | March 20, 2026, 8:50 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69bdb3a0bf908190b9a029f47e6be941 |
completed | March 20, 2026, 8:52 p.m. |
Created at: March 20, 2026, 1:04 p.m.