Triple

T15860179
Position Surface form Disambiguated ID Type / Status
Subject Hilbert–Schmidt operator E384562 entity
Predicate definedOn P4464 FINISHED
Object Hilbert space E2126 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: Hilbert space | Statement: [Hilbert–Schmidt operator, definedOn, Hilbert space]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hilbert space
Context triple: [Hilbert–Schmidt operator, definedOn, Hilbert space]
  • A. Hilbert spaces chosen
    Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
  • B. Banach spaces
    Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
  • C. Gelfand triples (rigged Hilbert spaces)
    Gelfand triples (rigged Hilbert spaces) are a mathematical framework that extends Hilbert spaces to rigorously handle generalized eigenvectors and distributions, particularly in quantum mechanics and functional analysis.
  • D. Schwartz space
    Schwartz space is the function space of rapidly decreasing smooth functions on Euclidean space, fundamental in distribution theory and Fourier analysis.
  • E. 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.
  • 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_69d86da422088190aac39e32e6c68429 completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e1555a1f008190bb3f03b0f35ed8a4 completed April 16, 2026, 9:32 p.m.
NED1 Entity disambiguation (via context triple) batch_69ffa14da7ac8190bbef49a1602a76fe completed May 9, 2026, 9:04 p.m.
Created at: April 10, 2026, 4:50 a.m.