Triple
T17341127
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Banach–Stone theorem |
E421067
|
entity |
| Predicate | hasGeneralization |
P2372
|
FINISHED |
| Object | Gelfand–Naimark theorem |
E270382
|
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: Gelfand–Naimark theorem | Statement: [Banach–Stone theorem, hasGeneralization, Gelfand–Naimark theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Gelfand–Naimark theorem Context triple: [Banach–Stone theorem, hasGeneralization, Gelfand–Naimark theorem]
-
A.
Gelfand–Naimark theorem
chosen
The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
-
B.
Gelfand–Naimark–Segal construction
The Gelfand–Naimark–Segal construction is a fundamental procedure in functional analysis that represents abstract C*-algebras as concrete operators on a Hilbert space via states, forming the basis of the GNS representation.
-
C.
Banach–Stone theorem
The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
-
D.
Stone–von Neumann theorem
The Stone–von Neumann theorem is a fundamental result in functional analysis and quantum mechanics that classifies all irreducible unitary representations of the canonical commutation relations as being unitarily equivalent.
-
E.
Scott–Mazur theorem
The Scott–Mazur theorem is a result in functional analysis that characterizes when a Banach space is reflexive in terms of the weak compactness of its closed unit ball.
- 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_69d889d3adc881909319f1edb8d2a956 |
completed | April 10, 2026, 5:25 a.m. |
| NER | Named-entity recognition | batch_69e43a15f6488190ad7d489e7391ab12 |
completed | April 19, 2026, 2:12 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a018c588a7081909ab108cb4adfedfe |
completed | May 11, 2026, 7:59 a.m. |
Created at: April 10, 2026, 5:44 a.m.