Triple
T17752485
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Racah algebra |
E443146
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Racah polynomials |
—
|
NE NERFINISHED |
How this triple was built (3 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: Racah polynomials | Statement: [Racah algebra, relatedTo, Racah polynomials]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Racah polynomials Context triple: [Racah algebra, relatedTo, Racah polynomials]
-
A.
Jacobi polynomials
Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
-
B.
Racah algebra
Racah algebra is a mathematical structure in representation theory and quantum mechanics that encodes the symmetries and coupling properties of angular momenta, particularly through Racah coefficients and related special functions.
-
C.
Jack polynomials
Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
-
D.
Gegenbauer polynomials
Gegenbauer polynomials are a family of orthogonal polynomials on the interval [-1, 1] that generalize Legendre polynomials and play a key role in harmonic analysis and solutions of differential equations with spherical symmetry.
-
E.
Orthogonal Polynomials
Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Racah polynomials Target entity description: Racah polynomials are a family of classical orthogonal polynomials that arise in the representation theory of angular momentum and in the study of exactly solvable models in mathematical physics.
-
A.
Jacobi polynomials
Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
-
B.
Racah algebra
Racah algebra is a mathematical structure in representation theory and quantum mechanics that encodes the symmetries and coupling properties of angular momenta, particularly through Racah coefficients and related special functions.
-
C.
Jack polynomials
Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
-
D.
Gegenbauer polynomials
Gegenbauer polynomials are a family of orthogonal polynomials on the interval [-1, 1] that generalize Legendre polynomials and play a key role in harmonic analysis and solutions of differential equations with spherical symmetry.
-
E.
Orthogonal Polynomials
Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
- F. None of above. chosen
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_69d8b9edf16c8190a59ebd245d378f4f |
completed | April 10, 2026, 8:50 a.m. |
| NER | Named-entity recognition | batch_69e4841c0540819093a32d759775c61f |
completed | April 19, 2026, 7:28 a.m. |
Created at: April 10, 2026, 10:10 a.m.