Triple

T11411529
Position Surface form Disambiguated ID Type / Status
Subject Gelfand representation of commutative C*-algebras E270381 entity
Predicate centralTo P164 FINISHED
Object Gelfand–Naimark theorem for commutative C*-algebras 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 for commutative C*-algebras | Statement: [Gelfand representation of commutative C*-algebras, centralTo, Gelfand–Naimark theorem for commutative C*-algebras]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Gelfand–Naimark theorem for commutative C*-algebras
Context triple: [Gelfand representation of commutative C*-algebras, centralTo, Gelfand–Naimark theorem for commutative C*-algebras]
  • A. 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.
  • B. 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).
  • 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’s theorem on one-parameter unitary groups
    Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
  • 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.
  • 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_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.
Created at: April 8, 2026, 9:34 p.m.