Triple

T18480351
Position Surface form Disambiguated ID Type / Status
Subject Szegő limit theorem E451539 entity
Predicate relatedTo P37 FINISHED
Object Wiener–Hopf factorization — 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: Wiener–Hopf factorization | Statement: [Szegő limit theorem, relatedTo, Wiener–Hopf factorization]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Wiener–Hopf factorization
Context triple: [Szegő limit theorem, relatedTo, Wiener–Hopf factorization]
  • A. Wiener–Hopf equations chosen
    Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
  • B. Pisier’s factorization theorems
    Pisier’s factorization theorems are fundamental results in functional analysis and operator theory that provide deep factorization properties for linear and multilinear operators on Banach spaces, extending and refining ideas related to Grothendieck-type inequalities.
  • C. Kailath factorization in linear systems
    Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
  • 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. Paley–Wiener theorem
    The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
  • 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.