Triple

T11411567
Position Surface form Disambiguated ID Type / Status
Subject Gelfand–Naimark theorem E270382 entity
Predicate hasFormulation P3660 FINISHED
Object noncommutative Gelfand–Naimark theorem E286300 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: noncommutative Gelfand–Naimark theorem | Statement: [Gelfand–Naimark theorem, hasFormulation, noncommutative Gelfand–Naimark theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: noncommutative Gelfand–Naimark theorem
Context triple: [Gelfand–Naimark theorem, hasFormulation, noncommutative Gelfand–Naimark theorem]
  • 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. von Neumann algebras
    Von Neumann algebras are operator algebras of bounded operators on a Hilbert space that are closed in the weak operator topology and under taking adjoints, forming a central object in functional analysis and quantum theory.
  • D. 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.
  • E. noncommutative geometry chosen
    Noncommutative geometry is a branch of mathematics that generalizes geometric concepts to settings where coordinate algebras do not commute, with deep applications in operator algebras, topology, and theoretical physics.
  • 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.