Triple

T940258
Position Surface form Disambiguated ID Type / Status
Subject Karl Weierstrass E20288 entity
Predicate notableFor P22 FINISHED
Object 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.
E110605 NE FINISHED

How this triple was built (4 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: [Karl Weierstrass, notableFor, Weierstrass approximation theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Weierstrass approximation theorem
Context triple: [Karl Weierstrass, notableFor, Weierstrass approximation theorem]
  • A. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • B. Brouwer fixed-point theorem
    The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
  • C. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
    Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
  • D. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • E. Berry–Esseen theorem
    The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Weierstrass approximation theorem
Triple: [Karl Weierstrass, notableFor, Weierstrass approximation theorem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Weierstrass approximation theorem
Target entity description: 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.
  • A. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • B. Brouwer fixed-point theorem
    The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
  • C. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
    Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
  • D. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • E. Berry–Esseen theorem
    The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
  • F. None of above. chosen

Provenance (5 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_69a493b0270c81909e6c9ce310f6aa55 completed March 1, 2026, 7:29 p.m.
NER Named-entity recognition batch_69a4b38b7da08190ac0853655dab678a completed March 1, 2026, 9:45 p.m.
NED1 Entity disambiguation (via context triple) batch_69a826e30c448190acc1457a63d27a4a completed March 4, 2026, 12:34 p.m.
NEDg Description generation batch_69a8343e16908190af102cfce025c31f completed March 4, 2026, 1:31 p.m.
NED2 Entity disambiguation (via description) batch_69a834f3a9288190a8cd28165379cec6 completed March 4, 2026, 1:34 p.m.
Created at: March 1, 2026, 7:40 p.m.