Triple

T14314167
Position Surface form Disambiguated ID Type / Status
Subject Bernstein inequalities E354909 entity
Predicate hasVariant P455 FINISHED
Object Bernstein inequality for polynomials E354909 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 inequality for polynomials | Statement: [Bernstein inequalities, hasVariant, Bernstein inequality for polynomials]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Bernstein inequality for polynomials
Context triple: [Bernstein inequalities, hasVariant, Bernstein inequality for polynomials]
  • A. Bernstein inequalities chosen
    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.
  • B. 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.
  • C. Inequalities for analytic functions
    "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
  • D. Hermite–Biehler theorem
    The Hermite–Biehler theorem is a result in complex analysis and control theory that characterizes when a complex polynomial has all its zeros in the open upper half-plane in terms of the interlacing of zeros of two associated real polynomials.
  • E. Carathéodory–Fejér interpolation
    Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
  • 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.