Triple

T4996522
Position Surface form Disambiguated ID Type / Status
Subject Weierstrass preparation theorem E112259 entity
Predicate involvesConcept P531 FINISHED
Object Weierstrass polynomial E112259 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: Weierstrass polynomial | Statement: [Weierstrass preparation theorem, involvesConcept, Weierstrass polynomial]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Weierstrass polynomial
Context triple: [Weierstrass preparation theorem, involvesConcept, Weierstrass polynomial]
  • A. Weierstrass preparation theorem chosen
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • 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. Weierstrass elliptic functions
    Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
  • D. Weierstrass function
    The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
  • E. Weierstrass factorization theorem
    The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
  • 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_69bd4432b32c81909f3b3c6bd10f0653 completed March 20, 2026, 12:57 p.m.
NER Named-entity recognition batch_69bd72a130708190b9bc1393ba78bfb1 completed March 20, 2026, 4:15 p.m.
NED1 Entity disambiguation (via context triple) batch_69be8a3489f08190a338de8d8be09813 completed March 21, 2026, 12:08 p.m.
Created at: March 20, 2026, 1:34 p.m.