Triple

T16284155
Position Surface form Disambiguated ID Type / Status
Subject Juliusz Schauder E395345 entity
Predicate notableWork P4 FINISHED
Object Schauder basis E412930 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: Schauder basis | Statement: [Juliusz Schauder, notableWork, Schauder basis]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Schauder basis
Context triple: [Juliusz Schauder, notableWork, Schauder basis]
  • A. Schauder basis chosen
    A Schauder basis is a sequence in a Banach space such that every element of the space can be uniquely represented as a convergent infinite linear combination of the sequence’s vectors.
  • B. Riesz basis
    A Riesz basis is a sequence in a Hilbert space that is complete and behaves like an orthonormal basis up to a bounded, invertible linear transformation, allowing stable and unique expansions of vectors.
  • 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. Hilbert spaces
    Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
  • 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_69d87f22c7248190a54c949738441e2e completed April 10, 2026, 4:40 a.m.
NER Named-entity recognition batch_69e24912c5808190a0d9c9f491315068 completed April 17, 2026, 2:52 p.m.
NED1 Entity disambiguation (via context triple) batch_6a0017c8f51c8190b73cdf2834eda57f completed May 10, 2026, 5:29 a.m.
Created at: April 10, 2026, 5:05 a.m.