Triple

T5425400
Position Surface form Disambiguated ID Type / Status
Subject Schauder fixed-point theorem E121350 entity
Predicate appliesTo P1129 FINISHED
Object Banach spaces E87729 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: Banach spaces | Statement: [Schauder fixed-point theorem, appliesTo, Banach spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Banach spaces
Context triple: [Schauder fixed-point theorem, appliesTo, Banach spaces]
  • A. Banach spaces chosen
    Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
  • B. Banach algebra
    A Banach algebra is a complete normed vector space equipped with a compatible associative algebra multiplication, allowing analysis and algebra to be combined in a single structure.
  • C. Hilbert spaces
    Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
  • D. Orlicz spaces
    Orlicz spaces are a class of function spaces that generalize Lebesgue spaces by measuring integrability via convex Orlicz functions rather than fixed power exponents.
  • E. Lebesgue spaces
    Lebesgue spaces are function spaces, denoted \(L^p\), that consist of measurable functions whose absolute values raised to the \(p\)-th power are integrable, forming a fundamental framework in modern analysis and probability 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_69bd463b58d88190b258261573de9e91 completed March 20, 2026, 1:06 p.m.
NER Named-entity recognition batch_69bd881598448190a9bb456dee36004b completed March 20, 2026, 5:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69bf3abfc7e88190b8f0a31b61c33973 completed March 22, 2026, 12:41 a.m.
Created at: March 20, 2026, 2:06 p.m.