Triple
T33761300
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jacobi ensemble |
E865110
|
entity |
| Predicate | hasOrthogonalPolynomialSystem |
P196514
|
FINISHED |
| Object | Jacobi polynomials with respect to w(x)=x^{α}(1-x)^{γ} |
—
|
LITERAL 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: Jacobi polynomials with respect to w(x)=x^{α}(1-x)^{γ} | Statement: [Jacobi ensemble, hasOrthogonalPolynomialSystem, Jacobi polynomials with respect to w(x)=x^{α}(1-x)^{γ}]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasOrthogonalPolynomialSystem
Context triple: [Jacobi ensemble, hasOrthogonalPolynomialSystem, Jacobi polynomials with respect to w(x)=x^{α}(1-x)^{γ}]
-
A.
hasAssociatedPolynomial
Indicates that one entity is linked to another entity that serves as its associated polynomial, typically representing or characterizing some of its properties or behavior.
-
B.
hasCharacteristicPolynomial
Indicates that one mathematical object (typically a matrix or linear operator) is associated with a specific characteristic polynomial that encodes its eigenvalue-related properties.
-
C.
arePolynomialsIn
Indicates that the specified expressions are polynomials in the given variable(s) or over the given ring/field.
-
D.
appliesToPolynomialsOf
Indicates that a rule, operation, or property is defined for and relevant to polynomials of a specified type or form.
-
E.
supportsSymbolicPolynomials
Indicates that an entity is capable of handling or operating on polynomials represented symbolically rather than as purely numeric values.
- F. None of above. chosen
Provenance (4 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_69f3498d3b748190aa3c4006c1f32f38 |
completed | April 30, 2026, 12:22 p.m. |
| NER | Named-entity recognition | batch_69fe59d11e9881909d2f33b7c717030e |
completed | May 8, 2026, 9:46 p.m. |
| PD | Predicate disambiguation | batch_69fe394fdfbc8190a931926ae3635cbf |
completed | May 8, 2026, 7:28 p.m. |
| PDg | Predicate description generation | batch_69fe59d03a648190bbe846cb5730a477 |
completed | May 8, 2026, 9:46 p.m. |
Created at: May 1, 2026, 1:45 a.m.