Triple

T17341127
Position Surface form Disambiguated ID Type / Status
Subject Banach–Stone theorem E421067 entity
Predicate hasGeneralization P2372 FINISHED
Object Gelfand–Naimark theorem 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 | Statement: [Banach–Stone theorem, hasGeneralization, Gelfand–Naimark theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gelfand–Naimark theorem
Context triple: [Banach–Stone theorem, hasGeneralization, Gelfand–Naimark theorem]
  • A. 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).
  • B. 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.
  • 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–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.
  • E. Scott–Mazur theorem
    The Scott–Mazur theorem is a result in functional analysis that characterizes when a Banach space is reflexive in terms of the weak compactness of its closed unit ball.
  • 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.