Triple

T11411565
Position Surface form Disambiguated ID Type / Status
Subject Gelfand–Naimark theorem E270382 entity
Predicate hasVariant P455 FINISHED
Object 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.
E924198 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–Segal construction | Statement: [Gelfand–Naimark theorem, hasVariant, Gelfand–Naimark–Segal construction]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gelfand–Naimark–Segal construction
Context triple: [Gelfand–Naimark theorem, hasVariant, Gelfand–Naimark–Segal construction]
  • A. 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).
  • B. Gelfand representation of commutative C*-algebras
    The Gelfand representation of commutative C*-algebras is a fundamental theorem in functional analysis that identifies any commutative C*-algebra with the algebra of continuous complex-valued functions on a compact Hausdorff space, its spectrum.
  • C. 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.
  • D. Atiyah–Segal axioms
    The Atiyah–Segal axioms are a set of mathematical conditions that rigorously define topological quantum field theories as functorial assignments from geometric data to algebraic structures.
  • E. Gelfand transform
    The Gelfand transform is a fundamental construction in functional analysis that represents elements of a commutative Banach algebra as continuous functions on its space of maximal ideals, linking algebraic structure with topological and spectral properties.
  • 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–Segal construction
Triple: [Gelfand–Naimark theorem, hasVariant, Gelfand–Naimark–Segal construction]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gelfand–Naimark–Segal construction
Target entity description: 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.
  • A. 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).
  • B. Gelfand representation of commutative C*-algebras
    The Gelfand representation of commutative C*-algebras is a fundamental theorem in functional analysis that identifies any commutative C*-algebra with the algebra of continuous complex-valued functions on a compact Hausdorff space, its spectrum.
  • C. 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.
  • D. Atiyah–Segal axioms
    The Atiyah–Segal axioms are a set of mathematical conditions that rigorously define topological quantum field theories as functorial assignments from geometric data to algebraic structures.
  • E. Gelfand transform
    The Gelfand transform is a fundamental construction in functional analysis that represents elements of a commutative Banach algebra as continuous functions on its space of maximal ideals, linking algebraic structure with topological and spectral properties.
  • 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_69d6aaddeaa8819088b30ef7b50598c9 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d8015017d08190b4020c76545556d6 completed April 9, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_69e5b855f0508190a2e57ef9407ddb1a completed April 20, 2026, 5:23 a.m.
NEDg Description generation batch_69e5c28d3824819097ff84cb4e13c923 completed April 20, 2026, 6:07 a.m.
NED2 Entity disambiguation (via description) batch_69e5c451c6c88190bcbb1f54ede35d29 completed April 20, 2026, 6:14 a.m.
Created at: April 8, 2026, 9:34 p.m.