Triple

T18480214
Position Surface form Disambiguated ID Type / Status
Subject Toeplitz matrix E451536 entity
Predicate relatedTo P37 FINISHED
Object Szegő limit theorem 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: Szegő limit theorem | Statement: [Toeplitz matrix, relatedTo, Szegő limit theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Szegő limit theorem
Context triple: [Toeplitz matrix, relatedTo, Szegő limit theorem]
  • A. Szegő limit theorem chosen
    The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
  • B. Szegő polynomials
    Szegő polynomials are a fundamental family of orthogonal polynomials on the unit circle that play a key role in complex analysis, approximation theory, and spectral theory.
  • C. Szegő kernel
    The Szegő kernel is a fundamental reproducing kernel in complex analysis and operator theory, associated with Hardy spaces on the boundary of a domain and central to the study of orthogonal polynomials and boundary behavior of analytic functions.
  • D. Tauberian theorems
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • E. Fisher–Hartwig conjecture
    The Fisher–Hartwig conjecture is a result in mathematical analysis that predicts the asymptotic behavior of Toeplitz determinants with singular symbols, extending the classical Szegő limit theorem.
  • 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53066a7108190a50eda9b489c90ca completed April 19, 2026, 7:43 p.m.
Created at: April 10, 2026, 11:35 a.m.