Triple
T2475510
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Israel Gelfand |
E55078
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Gelfand–Naimark theorem
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).
|
E270382
|
NE FINISHED |
How this triple was built (4 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: [Israel Gelfand, knownFor, Gelfand–Naimark theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Gelfand–Naimark theorem Context triple: [Israel Gelfand, knownFor, Gelfand–Naimark theorem]
-
A.
Alexandrov–Hausdorff theorem
The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
-
B.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
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.
Banach inverse mapping theorem
The Banach inverse mapping theorem is a fundamental result in functional analysis stating that a bijective bounded linear operator between Banach spaces has a bounded linear inverse.
-
E.
Osterwalder–Schrader axioms
The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Gelfand–Naimark theorem Triple: [Israel Gelfand, knownFor, Gelfand–Naimark theorem]
Generated description
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).
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Gelfand–Naimark theorem Target entity description: 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).
-
A.
Alexandrov–Hausdorff theorem
The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
-
B.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
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.
Banach inverse mapping theorem
The Banach inverse mapping theorem is a fundamental result in functional analysis stating that a bijective bounded linear operator between Banach spaces has a bounded linear inverse.
-
E.
Osterwalder–Schrader axioms
The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
- F. None of above. chosen
Provenance (5 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_69ab49e279e88190ab10d7248aea9d11 |
completed | March 6, 2026, 9:40 p.m. |
| NER | Named-entity recognition | batch_69abd14c8c388190bbdc486ffed6899e |
completed | March 7, 2026, 7:18 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69af17ab837881909bf8704acf9598e4 |
completed | March 9, 2026, 6:55 p.m. |
| NEDg | Description generation | batch_69af1a8c7784819088be431513d60325 |
completed | March 9, 2026, 7:07 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69af1b10738881909b296ecd3ff53c1b |
completed | March 9, 2026, 7:10 p.m. |
Created at: March 6, 2026, 9:45 p.m.