Triple
T12797503
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Functional analysis |
E305927
|
entity |
| Predicate | fieldOfStudy |
P3
|
FINISHED |
| Object | Hilbert spaces |
E2126
|
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: Hilbert spaces | Statement: [Functional analysis, fieldOfStudy, Hilbert spaces]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hilbert spaces Context triple: [Functional analysis, fieldOfStudy, Hilbert spaces]
-
A.
Hilbert spaces
chosen
Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
-
B.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
-
C.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
-
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.
Gelfand triples (rigged Hilbert spaces)
Gelfand triples (rigged Hilbert spaces) are a mathematical framework that extends Hilbert spaces to rigorously handle generalized eigenvectors and distributions, particularly in quantum mechanics and functional analysis.
- 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_69d7bdf366888190a8cccb982606889c |
completed | April 9, 2026, 2:55 p.m. |
| NER | Named-entity recognition | batch_69d96e6db68481909a2ca8da1287f3e0 |
completed | April 10, 2026, 9:41 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f6850d6ebc8190aaffcac09f4b15eb |
completed | May 2, 2026, 11:13 p.m. |
Created at: April 9, 2026, 5:30 p.m.