Triple

T17020362
Position Surface form Disambiguated ID Type / Status
Subject Schauder basis E412930 entity
Predicate relatedTo P37 FINISHED
Object Banach–Mazur theorem on bases E421069 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–Mazur theorem on bases | Statement: [Schauder basis, relatedTo, Banach–Mazur theorem on bases]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Banach–Mazur theorem on bases
Context triple: [Schauder basis, relatedTo, Banach–Mazur theorem on bases]
  • A. Banach–Mazur theorem chosen
    The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
  • B. Schreier family in Banach space theory
    The Schreier family in Banach space theory is a combinatorial collection of finite subsets of natural numbers introduced by Józef Schreier that plays a central role in constructing and analyzing special Banach spaces with unusual structural properties.
  • C. Gowers dichotomy for Banach spaces
    Gowers dichotomy for Banach spaces is a fundamental result in functional analysis that classifies infinite-dimensional Banach spaces by showing that each contains either a subspace with an unconditional basis or a hereditarily indecomposable subspace.
  • D. Mazur’s theorem on convex sets
    Mazur’s theorem on convex sets is a fundamental result in functional analysis that characterizes the structure and approximation properties of convex sets in Banach spaces, particularly via convex combinations of sequences.
  • E. 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.
  • 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_69d886cc4170819093deddc7b8b4b6a7 completed April 10, 2026, 5:12 a.m.
NER Named-entity recognition batch_69e3d482c3a0819099e6ea4acb0a08ee completed April 18, 2026, 6:59 p.m.
NED1 Entity disambiguation (via context triple) batch_6a011b4f9dfc819085639edb5cda1cca completed May 10, 2026, 11:57 p.m.
Created at: April 10, 2026, 5:33 a.m.