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.