Triple

T23142501
Position Surface form Disambiguated ID Type / Status
Subject graph Laplacian E577498 entity
Predicate alsoKnownAs P39 FINISHED
Object Laplacian matrix — 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: Laplacian matrix | Statement: [graph Laplacian, alsoKnownAs, Laplacian matrix]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Laplacian matrix
Context triple: [graph Laplacian, alsoKnownAs, Laplacian matrix]
  • A. graph Laplacian chosen
    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.
  • 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. 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.
  • D. matrix-tree theorem
    The matrix-tree theorem is a fundamental result in algebraic graph theory that expresses the number of spanning trees of a graph as a determinant of a matrix derived from the graph’s Laplacian.
  • E. Laplace operator
    The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
  • 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.