Triple

T7921600
Position Surface form Disambiguated ID Type / Status
Subject Jacobi matrix E183956 entity
Predicate usedIn P98 FINISHED
Object Golub–Kahan bidiagonalization E440653 NE FINISHED

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: Golub–Kahan bidiagonalization | Statement: [Jacobi matrix, usedIn, Golub–Kahan bidiagonalization]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Golub–Kahan bidiagonalization
Context triple: [Jacobi matrix, usedIn, Golub–Kahan bidiagonalization]
  • A. Toeplitz matrices
    Toeplitz matrices are structured matrices whose entries are constant along each diagonal, playing a central role in operator theory, numerical analysis, and signal processing.
  • B. Richardson iteration
    Richardson iteration is an early iterative method for solving linear systems and other operator equations, based on repeated relaxation steps to progressively improve an approximate solution.
  • C. Schmidt orthogonalization
    Schmidt orthogonalization is a mathematical procedure, also known as the Gram–Schmidt process, that converts a set of linearly independent vectors into an orthonormal set spanning the same subspace.
  • D. Tucker decomposition in multilinear algebra
    Tucker decomposition in multilinear algebra is a form of higher-order principal component analysis that factorizes a tensor into a core tensor multiplied by factor matrices along each mode, enabling dimensionality reduction and structure discovery in multiway data.
  • E. Bidiagonal chosen
    Bidiagonal is a special kind of sparse matrix that has nonzero entries only on the main diagonal and either the superdiagonal or subdiagonal, making it efficient for numerical linear algebra computations.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69ca828efbe48190bd48482650182e79 completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb3a9499cc8190b6bd81f4625c77ab completed March 31, 2026, 3:08 a.m.
NED1 Entity disambiguation (via context triple) batch_69cb5beea7988190972f7d02881d98f6 completed March 31, 2026, 5:30 a.m.
Created at: March 30, 2026, 5:06 p.m.