Triple
T17020322
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Banach algebra |
E412929
|
entity |
| Predicate | hasSubClass |
P21666
|
FINISHED |
| Object |
Banach *-algebra
A Banach *-algebra is a Banach algebra equipped with an involution operation that is continuous and compatible with the algebraic structure.
|
E1247129
|
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: Banach *-algebra | Statement: [Banach algebra, hasSubClass, Banach *-algebra]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Banach *-algebra Context triple: [Banach algebra, hasSubClass, Banach *-algebra]
-
A.
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.
-
B.
C*-algebras
C*-algebras are a class of norm-closed, self-adjoint operator algebras on Hilbert spaces that form a fundamental framework in functional analysis and noncommutative geometry.
-
C.
B(H), the algebra of all bounded operators on a Hilbert space H
B(H) is the canonical C*-algebra consisting of all bounded linear operators on a Hilbert space, serving as a fundamental example in operator algebras and functional analysis.
-
D.
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.
-
E.
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).
- 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: Banach *-algebra Triple: [Banach algebra, hasSubClass, Banach *-algebra]
Generated description
A Banach *-algebra is a Banach algebra equipped with an involution operation that is continuous and compatible with the algebraic structure.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Banach *-algebra Target entity description: A Banach *-algebra is a Banach algebra equipped with an involution operation that is continuous and compatible with the algebraic structure.
-
A.
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.
-
B.
C*-algebras
C*-algebras are a class of norm-closed, self-adjoint operator algebras on Hilbert spaces that form a fundamental framework in functional analysis and noncommutative geometry.
-
C.
B(H), the algebra of all bounded operators on a Hilbert space H
B(H) is the canonical C*-algebra consisting of all bounded linear operators on a Hilbert space, serving as a fundamental example in operator algebras and functional analysis.
-
D.
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.
-
E.
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).
- 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_69d886cc4170819093deddc7b8b4b6a7 |
completed | April 10, 2026, 5:12 a.m. |
| NER | Named-entity recognition | batch_69e3d482c3a0819099e6ea4acb0a08ee |
completed | April 18, 2026, 6:59 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a011b4f9dfc819085639edb5cda1cca |
completed | May 10, 2026, 11:57 p.m. |
| NEDg | Description generation | batch_6a011cc1afc48190b83e3203407c1d7f |
completed | May 11, 2026, 12:03 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a011d67c82c8190b737406e8952eb2b |
completed | May 11, 2026, 12:05 a.m. |
Created at: April 10, 2026, 5:33 a.m.