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.