Triple
T14314177
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bernstein inequalities |
E354909
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Bernstein polynomials |
E480872
|
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: Bernstein polynomials | Statement: [Bernstein inequalities, relatedTo, Bernstein polynomials]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bernstein polynomials Context triple: [Bernstein inequalities, relatedTo, Bernstein polynomials]
-
A.
Bernstein polynomials
chosen
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.
-
B.
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.
-
C.
Chebyshev polynomials of the first kind
Chebyshev polynomials of the first kind are a classical family of orthogonal polynomials on the interval [-1, 1] that play a central role in approximation theory, numerical analysis, and spectral methods.
-
D.
Birkhoff interpolation
Birkhoff interpolation is a generalized form of polynomial interpolation that allows prescribing function and derivative values at selected points, not necessarily in a consecutive or complete pattern.
-
E.
Bernstein inequalities
Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
- 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_69d8278ed42c8190b9f882dcce611347 |
completed | April 9, 2026, 10:26 p.m. |
| NER | Named-entity recognition | batch_69de85b49e5481909b9ffab2d922e284 |
completed | April 14, 2026, 6:21 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd4687c6bc819088452892128c420e |
completed | May 8, 2026, 2:12 a.m. |
Created at: April 10, 2026, 1:12 a.m.