Triple

T12026972
Position Surface form Disambiguated ID Type / Status
Subject Connes embedding problem E286302 entity
Predicate relatedConcept P37 FINISHED
Object Connes embedding property E286302 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: Connes embedding property | Statement: [Connes embedding problem, relatedConcept, Connes embedding property]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Connes embedding property
Context triple: [Connes embedding problem, relatedConcept, Connes embedding property]
  • A. Connes embedding problem chosen
    The Connes embedding problem is a central open question in operator algebras and quantum theory that asks whether every separable II₁ factor can be approximated in a specific way by finite-dimensional matrix algebras.
  • B. 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.
  • 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. Gel'fand–Kirillov conjecture
    The Gel'fand–Kirillov conjecture is a statement in noncommutative algebra proposing that certain universal enveloping algebras of Lie algebras are birationally equivalent to Weyl algebras, linking their structure to that of algebras of differential operators.
  • E. Connes–Moscovici index theorem
    The Connes–Moscovici index theorem is a fundamental result in noncommutative geometry that generalizes the classical Atiyah–Singer index theorem to the setting of foliations and noncommutative spaces.
  • 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_69d6ab4669e48190b59246358b0383ab completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d903f02638819091e0cc0e93fa5ea7 completed April 10, 2026, 2:06 p.m.
NED1 Entity disambiguation (via context triple) batch_69f48b8111b88190a42a8904a2d26862 completed May 1, 2026, 11:16 a.m.
Created at: April 8, 2026, 9:47 p.m.