Triple

T19231165
Position Surface form Disambiguated ID Type / Status
Subject Runge approximation theorem E480873 entity
Predicate relatedTo P37 FINISHED
Object Weierstrass approximation theorem — 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: Weierstrass approximation theorem | Statement: [Runge approximation theorem, relatedTo, Weierstrass approximation theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Weierstrass approximation theorem
Context triple: [Runge approximation theorem, relatedTo, Weierstrass approximation theorem]
  • A. Weierstrass approximation theorem chosen
    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.
  • B. Stone–Weierstrass theorem
    The Stone–Weierstrass theorem is a fundamental result in functional analysis that characterizes when a subalgebra of continuous functions on a compact space is dense, thereby generalizing classical polynomial approximation results.
  • C. 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.
  • D. Mergelyan's theorem
    Mergelyan's theorem is a fundamental result in complex analysis stating that every function continuous on a compact subset of the complex plane with connected complement and holomorphic in its interior can be uniformly approximated by polynomials.
  • E. Runge approximation theorem
    The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
  • 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_69d8e8ccb8f48190ad420098e74fb1db completed April 10, 2026, 12:10 p.m.
NER Named-entity recognition batch_69e5fa9ce5e081909df994841ce476d5 completed April 20, 2026, 10:06 a.m.
Created at: April 10, 2026, 1:25 p.m.