Triple

T16249744
Position Surface form Disambiguated ID Type / Status
Subject Banach–Steinhaus theorem E394468 entity
Predicate isEquivalentTo P6530 FINISHED
Object principle of uniform boundedness in Banach spaces 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: principle of uniform boundedness in Banach spaces | Statement: [Banach–Steinhaus theorem, isEquivalentTo, principle of uniform boundedness in Banach spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: principle of uniform boundedness in Banach spaces
Context triple: [Banach–Steinhaus theorem, isEquivalentTo, principle of uniform boundedness in Banach spaces]
  • 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–Alaoglu theorem
    The Banach–Alaoglu theorem is a fundamental result in functional analysis stating that the closed unit ball in the dual of a normed space is compact in the weak-* topology.
  • C. Banach limit
    A Banach limit is a linear functional on the space of bounded sequences that extends the usual limit and assigns generalized “limits” to sequences that may not converge in the classical sense.
  • D. Banach–Saks theorem
    The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
  • E. 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.
  • 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_69d87f2171208190951025e526947816 completed April 10, 2026, 4:40 a.m.
NER Named-entity recognition batch_69e2459606f88190a53905186f7f73be completed April 17, 2026, 2:37 p.m.
NED1 Entity disambiguation (via context triple) batch_6a000ee568a48190835ce76f84461044 completed May 10, 2026, 4:51 a.m.
Created at: April 10, 2026, 5:04 a.m.