Triple
T4927278
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Weierstrass factorization theorem |
E110607
|
entity |
| Predicate | uses |
P98
|
FINISHED |
| Object |
Weierstrass primary factors
Weierstrass primary factors are specially constructed entire functions used as building blocks in the Weierstrass factorization of entire functions according to their zeros.
|
E110607
|
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 primary factors | Statement: [Weierstrass factorization theorem, uses, Weierstrass primary factors]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weierstrass primary factors Context triple: [Weierstrass factorization theorem, uses, Weierstrass primary factors]
-
A.
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.
-
B.
Weierstrass preparation theorem
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.
-
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.
Picard theorem
Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
-
E.
Cauchy–Hadamard theorem
The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
- 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 primary factors Triple: [Weierstrass factorization theorem, uses, Weierstrass primary factors]
Generated description
Weierstrass primary factors are specially constructed entire functions used as building blocks in the Weierstrass factorization of entire functions according to their zeros.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Weierstrass primary factors Target entity description: Weierstrass primary factors are specially constructed entire functions used as building blocks in the Weierstrass factorization of entire functions according to their zeros.
-
A.
Weierstrass factorization theorem
chosen
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.
-
B.
Weierstrass preparation theorem
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.
-
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.
Picard theorem
Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
-
E.
Cauchy–Hadamard theorem
The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
- F. None of above.
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_69bd4415190c8190817bee7ec9f9f944 |
completed | March 20, 2026, 12:56 p.m. |
| NER | Named-entity recognition | batch_69bd7036d8e88190bc4be2975160da23 |
completed | March 20, 2026, 4:05 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69be77ac88148190a51fa2e9085d6897 |
completed | March 21, 2026, 10:49 a.m. |
| NEDg | Description generation | batch_69be7847a378819081687ec783a8b862 |
completed | March 21, 2026, 10:51 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69be7915a26c81909b21a128daebf5b3 |
completed | March 21, 2026, 10:55 a.m. |
Created at: March 20, 2026, 1:30 p.m.