Triple
T4927283
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Weierstrass factorization theorem |
E110607
|
entity |
| Predicate | isRelatedTo |
P37
|
FINISHED |
| Object |
Hadamard factorization theorem
The Hadamard factorization theorem is a result in complex analysis that expresses entire functions of finite order as products determined by their zeros and a polynomial factor.
|
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: Hadamard factorization theorem | Statement: [Weierstrass factorization theorem, isRelatedTo, Hadamard factorization theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hadamard factorization theorem Context triple: [Weierstrass factorization theorem, isRelatedTo, Hadamard factorization theorem]
-
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.
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.
-
C.
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.
-
D.
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.
-
E.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
- 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: Hadamard factorization theorem Triple: [Weierstrass factorization theorem, isRelatedTo, Hadamard factorization theorem]
Generated description
The Hadamard factorization theorem is a result in complex analysis that expresses entire functions of finite order as products determined by their zeros and a polynomial factor.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hadamard factorization theorem Target entity description: The Hadamard factorization theorem is a result in complex analysis that expresses entire functions of finite order as products determined by their zeros and a polynomial factor.
-
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.
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.
-
C.
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.
-
D.
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.
-
E.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
- 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.