Triple

T12797517
Position Surface form Disambiguated ID Type / Status
Subject Functional analysis E305927 entity
Predicate fieldOfStudy P3 FINISHED
Object Fredholm operators E391903 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: Fredholm operators | Statement: [Functional analysis, fieldOfStudy, Fredholm operators]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fredholm operators
Context triple: [Functional analysis, fieldOfStudy, Fredholm operators]
  • A. Fredholm operator chosen
    A Fredholm operator is a bounded linear operator between Banach (or Hilbert) spaces with finite-dimensional kernel and cokernel and a closed range, characterized by its integer-valued index.
  • B. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • C. Steklov operator
    The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
  • D. Theory of Linear Operations
    Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
  • E. Fredholm modules
    Fredholm modules are algebraic-analytic structures in noncommutative geometry that generalize elliptic operators and encode K-homology classes for C*-algebras.
  • 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_69d7bdf366888190a8cccb982606889c completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d96e6db68481909a2ca8da1287f3e0 completed April 10, 2026, 9:41 p.m.
NED1 Entity disambiguation (via context triple) batch_69f6850d6ebc8190aaffcac09f4b15eb completed May 2, 2026, 11:13 p.m.
Created at: April 9, 2026, 5:30 p.m.