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.