Triple
T13893978
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hadamard matrix |
E334040
|
entity |
| Predicate | hasSpecialCase |
P7025
|
FINISHED |
| Object | Sylvester Hadamard matrix |
E334040
|
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: Sylvester Hadamard matrix | Statement: [Hadamard matrix, hasSpecialCase, Sylvester Hadamard matrix]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Sylvester Hadamard matrix Context triple: [Hadamard matrix, hasSpecialCase, Sylvester Hadamard matrix]
-
A.
Hadamard matrices
chosen
Hadamard matrices are square matrices with entries ±1 whose rows are mutually orthogonal, playing a key role in combinatorics, coding theory, and signal processing.
-
B.
Sylvester determinant
The Sylvester determinant is a mathematical construct introduced by James Joseph Sylvester, typically referring to a determinant associated with resultants and elimination theory in algebra.
-
C.
Hurwitz matrix
The Hurwitz matrix is a structured matrix constructed from the coefficients of a polynomial and used to determine system stability in control theory via the Routh–Hurwitz criterion.
-
D.
Cauchy matrix
A Cauchy matrix is a structured matrix whose entries are defined by the reciprocals of pairwise differences of two sequences, widely used in numerical analysis, interpolation, and algebra.
-
E.
Vandermonde matrix
A Vandermonde matrix is a structured matrix whose rows (or columns) are geometric progressions of given numbers, widely used in polynomial interpolation, determinant theory, and numerical analysis.
- 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_69d81c5dd2d48190b7a5fc1e009de936 |
completed | April 9, 2026, 9:38 p.m. |
| NER | Named-entity recognition | batch_69de23a741908190bdf46d76c5f1411a |
completed | April 14, 2026, 11:23 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f7c71ca8a881908ac02687fbfe62fb |
completed | May 3, 2026, 10:07 p.m. |
Created at: April 9, 2026, 10:15 p.m.