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.