Triple
T17676479
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bidiagonal matrix |
E440653
|
entity |
| Predicate | isUsedWith |
P4791
|
FINISHED |
| Object | Householder reflections |
—
|
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: Householder reflections | Statement: [Bidiagonal matrix, isUsedWith, Householder reflections]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Householder reflections Context triple: [Bidiagonal matrix, isUsedWith, Householder reflections]
-
A.
Householder transformation
chosen
The Householder transformation is a linear algebra technique that uses reflections to orthogonally transform vectors and matrices, commonly employed in QR decomposition and numerical algorithms.
-
B.
Jacobi eigenvalue algorithm
The Jacobi eigenvalue algorithm is an iterative numerical method for computing all eigenvalues and eigenvectors of a real symmetric matrix by applying a sequence of orthogonal similarity transformations.
-
C.
Bartels–Stewart algorithm
The Bartels–Stewart algorithm is a numerical linear algebra method that efficiently solves certain matrix equations, particularly Sylvester and Lyapunov equations, using Schur decompositions.
-
D.
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.
-
E.
Hermite normal form
Hermite normal form is a canonical matrix form used in linear algebra and number theory to uniquely represent integer matrices and solve systems of linear Diophantine equations.
- 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_69d8b9e940b081908b862bb0e6e89b0d |
completed | April 10, 2026, 8:50 a.m. |
| NER | Named-entity recognition | batch_69e46f6d9ab88190ab0e25eac8b0101c |
completed | April 19, 2026, 6 a.m. |
Created at: April 10, 2026, 10:01 a.m.