Triple

T21047258
Position Surface form Disambiguated ID Type / Status
Subject Lindelöf theorem in complex analysis E518479 entity
Predicate usedIn P98 FINISHED
Object Hardy space theory NE NERFINISHED

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: Hardy space theory | Statement: [Lindelöf theorem in complex analysis, usedIn, Hardy space theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hardy space theory
Context triple: [Lindelöf theorem in complex analysis, usedIn, Hardy space theory]
  • A. Hardy space chosen
    A Hardy space is a function space in complex analysis consisting of holomorphic functions on a domain whose mean values on boundary circles (or lines) are uniformly bounded, playing a central role in harmonic and operator theory.
  • B. Littlewood–Paley theory
    Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
  • C. Calderón–Zygmund theory
    Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
  • D. Dirichlet space
    Dirichlet space is a functional Hilbert space of analytic functions on the unit disk characterized by square-integrable derivatives, playing a central role in complex analysis and potential theory.
  • E. Herglotz functions
    Herglotz functions are analytic functions on the upper half-plane with nonnegative imaginary part, central in complex analysis and operator theory due to their integral representation and role in moment and interpolation problems.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e0b50438e08190917e2538bb8bc034 completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e6fcf4d26481908b639996500a8319 completed April 21, 2026, 4:28 a.m.
Created at: April 16, 2026, 2:34 p.m.