Triple

T10881060
Position Surface form Disambiguated ID Type / Status
Subject Methods of Mathematical Physics E256917 entity
Predicate hasTopic P531 FINISHED
Object Hilbert spaces 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 spaces | Statement: [Methods of Mathematical Physics, hasTopic, Hilbert spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hilbert spaces
Context triple: [Methods of Mathematical Physics, hasTopic, Hilbert spaces]
  • 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. 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.
  • D. Foundations of Functional Analysis
    Foundations of Functional Analysis is a seminal mathematical text that systematically develops the core concepts and theorems of functional analysis, particularly in the tradition of the Riesz school.
  • E. 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.
  • 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_69d6aa848804819081b2713ca0bedf06 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d751b031a88190b1182dfc1f520264 completed April 9, 2026, 7:13 a.m.
NED1 Entity disambiguation (via context triple) batch_69dff7e479cc81909fb8510364d6fc0e completed April 15, 2026, 8:41 p.m.
Created at: April 8, 2026, 9:21 p.m.