Triple

T9843849
Position Surface form Disambiguated ID Type / Status
Subject Cauchy–Schwarz inequality E239290 entity
Predicate appliesTo P1129 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: [Cauchy–Schwarz inequality, appliesTo, Hilbert spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hilbert spaces
Context triple: [Cauchy–Schwarz inequality, appliesTo, 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_69ca84e3f0c48190ada72a65ebd50efd completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb35dc29c819080203be5b904dc9d completed April 2, 2026, 12:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1d5dda4b0819092703270e87bee5a completed April 5, 2026, 3:24 a.m.
Created at: March 30, 2026, 8:33 p.m.