Triple

T4092294
Position Surface form Disambiguated ID Type / Status
Subject Banach space E87729 entity
Predicate hasConcept P531 FINISHED
Object Banach–Steinhaus theorem E394468 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–Steinhaus theorem | Statement: [Banach space, hasConcept, Banach–Steinhaus theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Banach–Steinhaus theorem
Context triple: [Banach space, hasConcept, Banach–Steinhaus theorem]
  • A. Banach–Steinhaus theorem chosen
    The Banach–Steinhaus theorem is a fundamental result in functional analysis that characterizes when a family of continuous linear operators is uniformly bounded, with major implications for the behavior of sequences of operators on Banach spaces.
  • B. Banach inverse mapping theorem
    The Banach inverse mapping theorem is a fundamental result in functional analysis stating that a bijective bounded linear operator between Banach spaces has a bounded linear inverse.
  • C. Riesz–Fischer theorem
    The Riesz–Fischer theorem is a fundamental result in functional analysis that establishes the equivalence between square-summable sequences and square-integrable functions, providing the foundation for the Hilbert space structure of L² spaces.
  • D. Gelfand–Naimark theorem
    The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
  • E. Schauder fixed-point theorem
    The Schauder fixed-point theorem is a fundamental result in functional analysis that guarantees the existence of fixed points for continuous compact mappings on convex closed subsets of Banach spaces, generalizing the Brouwer fixed-point theorem to infinite-dimensional settings.
  • 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_69aed94425148190be337845d56fac22 completed March 9, 2026, 2:29 p.m.
NER Named-entity recognition batch_69aefcae22a081908af65a960306b78c completed March 9, 2026, 5 p.m.
NED1 Entity disambiguation (via context triple) batch_69b56b6cfb288190ac08c3a37327ac9a completed March 14, 2026, 2:06 p.m.
Created at: March 9, 2026, 3:40 p.m.