Triple

T7491934
Position Surface form Disambiguated ID Type / Status
Subject Feshbach projection formalism E177025 entity
Predicate usesConcept P531 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: [Feshbach projection formalism, usesConcept, Hilbert space]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hilbert space
Context triple: [Feshbach projection formalism, usesConcept, 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. 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.
  • E. Riesz representation theorem
    The Riesz representation theorem is a fundamental result in functional analysis that characterizes continuous linear functionals on Hilbert spaces as inner products with a unique vector in the space.
  • 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_69c69f2583808190bd1a4936c42a5815 completed March 27, 2026, 3:15 p.m.
NER Named-entity recognition batch_69c6f5767d3481909a9a0e099cc02d03 completed March 27, 2026, 9:24 p.m.
NED1 Entity disambiguation (via context triple) batch_69c83c76a8988190bb5ff21731b19d4b completed March 28, 2026, 8:39 p.m.
Created at: March 27, 2026, 3:43 p.m.