Triple

T17341218
Position Surface form Disambiguated ID Type / Status
Subject Banach–Mazur theorem E421069 entity
Predicate relatedTo P37 FINISHED
Object Gelfand representation E270383 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 representation | Statement: [Banach–Mazur theorem, relatedTo, Gelfand representation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Gelfand representation
Context triple: [Banach–Mazur theorem, relatedTo, Gelfand representation]
  • A. Gelfand transform chosen
    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.
  • 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. 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.
  • D. 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).
  • E. Riesz representation theorem
    The Riesz representation theorem is a fundamental result in functional analysis that characterizes continuous linear functionals on Hilbert spaces as inner products with a unique vector in the space.
  • 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_69d889d3adc881909319f1edb8d2a956 completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e43a15f6488190ad7d489e7391ab12 completed April 19, 2026, 2:12 a.m.
NED1 Entity disambiguation (via context triple) batch_6a018c588a7081909ab108cb4adfedfe completed May 11, 2026, 7:59 a.m.
Created at: April 10, 2026, 5:44 a.m.