Triple

T10991936
Position Surface form Disambiguated ID Type / Status
Subject Montel's theorem E259771 entity
Predicate hasVariant P455 FINISHED
Object Montel's theorem for subharmonic functions E259771 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: Montel's theorem for subharmonic functions | Statement: [Montel's theorem, hasVariant, Montel's theorem for subharmonic functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Montel's theorem for subharmonic functions
Context triple: [Montel's theorem, hasVariant, Montel's theorem for subharmonic functions]
  • A. Montel theorem chosen
    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.
  • B. Lempert function on convex domains
    The Lempert function on convex domains is a complex-analytic invariant that coincides with the Kobayashi distance and provides an extremal characterization of holomorphic mappings between convex domains in several complex variables.
  • C. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • D. Hadamard three-circle theorem
    The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
  • E. Inequalities for analytic functions
    "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
  • 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e374639f1481908ea372b81a834f6f completed April 18, 2026, 12:09 p.m.
Created at: April 8, 2026, 9:24 p.m.