Triple

T22137949
Position Surface form Disambiguated ID Type / Status
Subject Sergei Natanovich Bernstein E547080 entity
Predicate notableConcept P201 FINISHED
Object Bernstein’s theorem in approximation theory — NE NERFINISHED

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’s theorem in approximation theory | Statement: [Sergei Natanovich Bernstein, notableConcept, Bernstein’s theorem in approximation theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Bernstein’s theorem in approximation theory
Context triple: [Sergei Natanovich Bernstein, notableConcept, Bernstein’s theorem in approximation theory]
  • 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. Favard's theorem
    Favard's theorem is a fundamental result in the theory of orthogonal polynomials that characterizes such polynomial sequences precisely as those satisfying a three-term recurrence relation with appropriate coefficients.
  • C. Weierstrass approximation theorem
    The Weierstrass approximation theorem is a fundamental result in real analysis stating that any continuous function on a closed interval can be uniformly approximated by polynomials.
  • D. 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.
  • E. Chebyshev alternation theorem
    The Chebyshev alternation theorem is a fundamental result in approximation theory that characterizes the best uniform (minimax) polynomial approximation to a continuous function by the presence of alternating maximum errors at a finite set of points.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

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_69e11e3a95d88190a3bd80d9471976c3 completed April 16, 2026, 5:36 p.m.
NER Named-entity recognition batch_69f129bb78bc8190b74af3a5f6a5348f completed April 28, 2026, 9:42 p.m.
Created at: April 16, 2026, 8:32 p.m.