Triple
T13660511
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Picard theorem |
E326981
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Casorati–Weierstrass theorem
The Casorati–Weierstrass theorem is a fundamental result in complex analysis stating that near an essential singularity, a complex function attains values arbitrarily close to every complex number.
|
E1055799
|
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: Casorati–Weierstrass theorem | Statement: [Picard theorem, relatedTo, Casorati–Weierstrass theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Casorati–Weierstrass theorem Context triple: [Picard theorem, relatedTo, Casorati–Weierstrass theorem]
-
A.
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.
-
B.
Montel theorem
Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
-
C.
Malgrange–Ehrenpreis theorem
The Malgrange–Ehrenpreis theorem is a fundamental result in the theory of partial differential equations stating that every linear partial differential operator with constant coefficients admits a fundamental solution.
-
D.
Corona theorem
The Corona theorem is a fundamental result in complex analysis that characterizes when bounded analytic functions on the unit disk can be solved in a certain type of division problem, showing that the maximal ideal space of the disk algebra has no "corona."
-
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. 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: Casorati–Weierstrass theorem Triple: [Picard theorem, relatedTo, Casorati–Weierstrass theorem]
Generated description
The Casorati–Weierstrass theorem is a fundamental result in complex analysis stating that near an essential singularity, a complex function attains values arbitrarily close to every complex number.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Casorati–Weierstrass theorem Target entity description: The Casorati–Weierstrass theorem is a fundamental result in complex analysis stating that near an essential singularity, a complex function attains values arbitrarily close to every complex number.
-
A.
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.
-
B.
Montel theorem
Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
-
C.
Malgrange–Ehrenpreis theorem
The Malgrange–Ehrenpreis theorem is a fundamental result in the theory of partial differential equations stating that every linear partial differential operator with constant coefficients admits a fundamental solution.
-
D.
Corona theorem
The Corona theorem is a fundamental result in complex analysis that characterizes when bounded analytic functions on the unit disk can be solved in a certain type of division problem, showing that the maximal ideal space of the disk algebra has no "corona."
-
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. 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_69d8076d8270819092afc2f0e9c359a8 |
completed | April 9, 2026, 8:09 p.m. |
| NER | Named-entity recognition | batch_69dbc620df208190afaccf3ddd10aa60 |
completed | April 12, 2026, 4:19 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f794395618819094a7f0ffcf5d3fb6 |
completed | May 3, 2026, 6:30 p.m. |
| NEDg | Description generation | batch_69f7986b9a1c8190b88634af9fc11ebe |
completed | May 3, 2026, 6:48 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69f798d7e1a0819087332287d5f9a25f |
completed | May 3, 2026, 6:50 p.m. |
Created at: April 9, 2026, 9:52 p.m.