Triple

T22666484
Position Surface form Disambiguated ID Type / Status
Subject Poisson kernel E559804 entity
Predicate connectedTo P37 FINISHED
Object Hardy spaces 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 spaces | Statement: [Poisson kernel, connectedTo, Hardy spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hardy spaces
Context triple: [Poisson kernel, connectedTo, Hardy spaces]
  • 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. Three regularity results in harmonic analysis
    "Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
  • C. 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.
  • 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. Jessen’s theorem in harmonic analysis
    Jessen’s theorem in harmonic analysis is a result that provides conditions under which certain trigonometric or Fourier series converge almost everywhere, reflecting Børge Jessen’s contributions to the study of convergence phenomena in harmonic analysis.
  • 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_69e2454a158c819093b8e35f5045efb6 completed April 17, 2026, 2:35 p.m.
NER Named-entity recognition batch_69f1781c2c808190baf6964ca1eced6f completed April 29, 2026, 3:16 a.m.
Created at: April 17, 2026, 3:09 p.m.