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.