Triple

T12138871
Position Surface form Disambiguated ID Type / Status
Subject Pafnuty Chebyshev E289130 entity
Predicate notableWork P4 FINISHED
Object Chebyshev’s equioscillation theorem E968219 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: Chebyshev’s equioscillation theorem | Statement: [Pafnuty Chebyshev, notableWork, Chebyshev’s equioscillation theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Chebyshev’s equioscillation theorem
Context triple: [Pafnuty Chebyshev, notableWork, Chebyshev’s equioscillation theorem]
  • A. Chebyshev alternation theorem chosen
    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.
  • B. 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.
  • C. Chebyshev rational approximation
    Chebyshev rational approximation is a mathematical technique that uses rational functions to approximate other functions with near-optimal uniform accuracy over a given interval.
  • D. 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.
  • 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_69d6ab4b5e4c81909950b17151eb0951 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9158eef48819083bdce283a363414 completed April 10, 2026, 3:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69f60a7baee88190a32a5a3cd0b8a326 completed May 2, 2026, 2:30 p.m.
Created at: April 8, 2026, 9:49 p.m.