Triple

T4927202
Position Surface form Disambiguated ID Type / Status
Subject Weierstrass approximation theorem E110605 entity
Predicate relatedTo P37 FINISHED
Object Stone–Weierstrass theorem E480871 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: Stone–Weierstrass theorem | Statement: [Weierstrass approximation theorem, relatedTo, Stone–Weierstrass theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Stone–Weierstrass theorem
Context triple: [Weierstrass approximation theorem, relatedTo, Stone–Weierstrass theorem]
  • A. Stone–Weierstrass theorem chosen
    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.
  • 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. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • D. Banach–Stone theorem
    The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
  • 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 (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_69bd4415190c8190817bee7ec9f9f944 completed March 20, 2026, 12:56 p.m.
NER Named-entity recognition batch_69bd70354bd081909291a43439f42ed3 completed March 20, 2026, 4:05 p.m.
NED1 Entity disambiguation (via context triple) batch_69be81c2cb288190b0a603992c08235c completed March 21, 2026, 11:32 a.m.
Created at: March 20, 2026, 1:30 p.m.