Triple
T16892564
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Banach–Alaoglu theorem |
E424210
|
entity |
| Predicate | domain |
P87
|
FINISHED |
| Object | Banach spaces |
E87729
|
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 spaces | Statement: [Banach–Alaoglu theorem, domain, Banach spaces]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Banach spaces Context triple: [Banach–Alaoglu theorem, domain, Banach spaces]
-
A.
Banach spaces
chosen
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
-
B.
Banach algebra
A Banach algebra is a complete normed vector space equipped with a compatible associative algebra multiplication, allowing analysis and algebra to be combined in a single structure.
-
C.
Hilbert spaces
Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
-
D.
Foundations of Functional Analysis
Foundations of Functional Analysis is a seminal mathematical text that systematically develops the core concepts and theorems of functional analysis, particularly in the tradition of the Riesz school.
-
E.
functional analysis
Functional analysis is a branch of mathematics that studies vector spaces with additional structure (such as norms or inner products) and the linear operators acting on them, often using tools from topology and measure theory.
- 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_69d889da3e8c8190a2b118f383f0beac |
completed | April 10, 2026, 5:25 a.m. |
| NER | Named-entity recognition | batch_69e3bbc5a5308190937ebd05356bd91d |
completed | April 18, 2026, 5:13 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a00c7a7fd8481908ef82a13418b1c2d |
completed | May 10, 2026, 6 p.m. |
Created at: April 10, 2026, 5:29 a.m.