Triple

T12026974
Position Surface form Disambiguated ID Type / Status
Subject Connes embedding problem E286302 entity
Predicate relatedConcept P37 FINISHED
Object Tsirelson problem
The Tsirelson problem is a fundamental question in quantum information theory asking whether two natural mathematical models of bipartite quantum correlations—tensor product and commuting operator models—always coincide.
E286302 NE FINISHED

How this triple was built (4 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: Tsirelson problem | Statement: [Connes embedding problem, relatedConcept, Tsirelson problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Tsirelson problem
Context triple: [Connes embedding problem, relatedConcept, Tsirelson problem]
  • A. 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.
  • B. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • C. Kochen–Specker theorem
    The Kochen–Specker theorem is a foundational result in quantum mechanics showing that it is impossible to assign consistent, noncontextual definite values to all quantum observables, thereby ruling out a broad class of hidden-variable theories.
  • D. Haag’s theorem
    Haag’s theorem is a result in axiomatic quantum field theory showing that the interaction picture cannot be consistently defined for interacting fields in the same Hilbert space as free fields, undermining the standard formulation of quantum field theory.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Tsirelson problem
Triple: [Connes embedding problem, relatedConcept, Tsirelson problem]
Generated description
The Tsirelson problem is a fundamental question in quantum information theory asking whether two natural mathematical models of bipartite quantum correlations—tensor product and commuting operator models—always coincide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Tsirelson problem
Target entity description: The Tsirelson problem is a fundamental question in quantum information theory asking whether two natural mathematical models of bipartite quantum correlations—tensor product and commuting operator models—always coincide.
  • 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. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • C. Kochen–Specker theorem
    The Kochen–Specker theorem is a foundational result in quantum mechanics showing that it is impossible to assign consistent, noncontextual definite values to all quantum observables, thereby ruling out a broad class of hidden-variable theories.
  • D. Haag’s theorem
    Haag’s theorem is a result in axiomatic quantum field theory showing that the interaction picture cannot be consistently defined for interacting fields in the same Hilbert space as free fields, undermining the standard formulation of quantum field theory.
  • E. 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.
  • F. None of above.

Provenance (5 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.
NEDg Description generation batch_69f48fc7a8848190a06b34cc45db4789 completed May 1, 2026, 11:34 a.m.
NED2 Entity disambiguation (via description) batch_69f495f069c48190a6e5856c272420c0 completed May 1, 2026, noon
Created at: April 8, 2026, 9:47 p.m.