Triple
T7705205
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Edgeworth expansion |
E174595
|
entity |
| Predicate | uses |
P98
|
FINISHED |
| Object |
Hermite polynomials
Hermite polynomials are a classical family of orthogonal polynomials that arise prominently in probability theory, mathematical physics, and approximation methods such as the Edgeworth expansion.
|
E502189
|
NE FINISHED |
How this triple was built (4 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: Hermite polynomials | Statement: [Edgeworth expansion, uses, Hermite polynomials]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hermite polynomials Context triple: [Edgeworth expansion, uses, Hermite polynomials]
-
A.
Hermite
Hermite is a French surname most famously associated with the 19th-century mathematician Charles Hermite, known for his contributions to number theory, algebra, and analysis.
-
B.
Hermite functions
Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
-
C.
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.
-
D.
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.
-
E.
Bernoulli polynomials
Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Hermite polynomials Triple: [Edgeworth expansion, uses, Hermite polynomials]
Generated description
Hermite polynomials are a classical family of orthogonal polynomials that arise prominently in probability theory, mathematical physics, and approximation methods such as the Edgeworth expansion.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hermite polynomials Target entity description: Hermite polynomials are a classical family of orthogonal polynomials that arise prominently in probability theory, mathematical physics, and approximation methods such as the Edgeworth expansion.
-
A.
Hermite
Hermite is a French surname most famously associated with the 19th-century mathematician Charles Hermite, known for his contributions to number theory, algebra, and analysis.
-
B.
Hermite functions
chosen
Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
-
C.
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.
-
D.
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.
-
E.
Bernoulli polynomials
Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
- F. None of above.
Provenance (5 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_69c6995b3e8c8190833108f883d5f53c |
completed | March 27, 2026, 2:51 p.m. |
| NER | Named-entity recognition | batch_69c7028f17f0819081686ac146750d3a |
completed | March 27, 2026, 10:19 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c8acc088148190ba5ba07e4ad2284c |
completed | March 29, 2026, 4:38 a.m. |
| NEDg | Description generation | batch_69c8ae313d4c8190964be233c0651f3a |
completed | March 29, 2026, 4:44 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c8aea55c0081909aa0f6c96c8d6a03 |
completed | March 29, 2026, 4:46 a.m. |
Created at: March 27, 2026, 4:03 p.m.