Triple

T19967329
Position Surface form Disambiguated ID Type / Status
Subject Herman Auerbach E479971 entity
Predicate notableFor P22 FINISHED
Object Auerbach bases in normed spaces
Auerbach bases in normed spaces are special bases in finite-dimensional normed vector spaces whose elements and corresponding coordinate functionals all have norm one, providing a norm-adapted analogue of orthonormal bases.
E1404141 NE FINISHED

How this triple was built (4 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: Auerbach bases in normed spaces | Statement: [Herman Auerbach, notableFor, Auerbach bases in normed spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Auerbach bases in normed spaces
Context triple: [Herman Auerbach, notableFor, Auerbach bases in normed spaces]
  • A. 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.
  • B. 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.
  • 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. New classes of Lp-spaces
    "New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Auerbach bases in normed spaces
Triple: [Herman Auerbach, notableFor, Auerbach bases in normed spaces]
Generated description
Auerbach bases in normed spaces are special bases in finite-dimensional normed vector spaces whose elements and corresponding coordinate functionals all have norm one, providing a norm-adapted analogue of orthonormal bases.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Auerbach bases in normed spaces
Target entity description: Auerbach bases in normed spaces are special bases in finite-dimensional normed vector spaces whose elements and corresponding coordinate functionals all have norm one, providing a norm-adapted analogue of orthonormal bases.
  • A. 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.
  • B. 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.
  • 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. New classes of Lp-spaces
    "New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
  • E. 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.
  • F. None of above. chosen

Provenance (5 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_69d8e523c19881909f9197037200dde6 completed April 10, 2026, 11:55 a.m.
NER Named-entity recognition batch_69e65bc5e41881908c1e8867820f1c0c completed April 20, 2026, 5 p.m.
NED1 Entity disambiguation (via context triple) batch_6a07fdd12e4c81908488a7a829ee7bc2 completed May 16, 2026, 5:17 a.m.
NEDg Description generation batch_6a07ff37a0508190af7cf7a045201338 completed May 16, 2026, 5:23 a.m.
NED2 Entity disambiguation (via description) batch_6a07ffad71508190a6636834b7f25434 completed May 16, 2026, 5:25 a.m.
Created at: April 10, 2026, 1:54 p.m.