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.