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.