Triple
T6293580
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bernoulli numbers |
E141076
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Bernoulli polynomials |
E583311
|
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: Bernoulli polynomials | Statement: [Bernoulli numbers, relatedTo, Bernoulli polynomials]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bernoulli polynomials Context triple: [Bernoulli numbers, relatedTo, Bernoulli polynomials]
-
A.
Bernoulli polynomials
chosen
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.
-
B.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
-
C.
Bernstein polynomials
Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
-
D.
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.
-
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.
- 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_69c008cdf2ac8190bb640c94478fb4ed |
completed | March 22, 2026, 3:20 p.m. |
| NER | Named-entity recognition | batch_69c06438654481908c9833c5f0d61773 |
completed | March 22, 2026, 9:50 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c603f715a08190b44156b4f5166631 |
completed | March 27, 2026, 4:13 a.m. |
Created at: March 22, 2026, 4:27 p.m.