Triple

T12026978
Position Surface form Disambiguated ID Type / Status
Subject Connes embedding problem E286302 entity
Predicate relatedConcept P37 FINISHED
Object von Neumann factors E14972 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: von Neumann factors | Statement: [Connes embedding problem, relatedConcept, von Neumann factors]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: von Neumann factors
Context triple: [Connes embedding problem, relatedConcept, von Neumann factors]
  • A. von Neumann algebras chosen
    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.
  • B. Connes embedding problem
    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.
  • C. Pisier’s factorization theorems
    Pisier’s factorization theorems are fundamental results in functional analysis and operator theory that provide deep factorization properties for linear and multilinear operators on Banach spaces, extending and refining ideas related to Grothendieck-type inequalities.
  • D. 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.
  • E. 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).
  • 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.