Triple

T12027031
Position Surface form Disambiguated ID Type / Status
Subject Noncommutative Geometry (1994 book) E286303 entity
Predicate subject P450 FINISHED
Object noncommutative tori
Noncommutative tori are fundamental examples of noncommutative spaces in operator algebras and noncommutative geometry, generalizing the algebra of functions on a classical torus by deforming the commutation relations of its coordinate functions.
 E959834 NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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 tori | Statement: [Noncommutative Geometry (1994 book), subject, noncommutative tori]

Disambiguation candidates (2 decisions)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: noncommutative tori
Context triple: [Noncommutative Geometry (1994 book), subject, noncommutative tori]
  • A. noncommutative geometry
    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.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Noncommutative Geometry, Quantum Fields and Motives
    Noncommutative Geometry, Quantum Fields and Motives is a seminal work by Alain Connes that develops a deep interplay between noncommutative geometry, quantum field theory, and arithmetic geometry through the language of motives.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: noncommutative tori
Target entity description: Noncommutative tori are fundamental examples of noncommutative spaces in operator algebras and noncommutative geometry, generalizing the algebra of functions on a classical torus by deforming the commutation relations of its coordinate functions.
  • A. noncommutative geometry
    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.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Noncommutative Geometry, Quantum Fields and Motives
    Noncommutative Geometry, Quantum Fields and Motives is a seminal work by Alain Connes that develops a deep interplay between noncommutative geometry, quantum field theory, and arithmetic geometry through the language of motives.
  • F. None of above. chosen

How the object was described

The object's one-sentence description was generated by prompting gpt-5.1 with the object name and this triple as context.

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: noncommutative tori
Triple: [Noncommutative Geometry (1994 book), subject, noncommutative tori]
Generated description
Noncommutative tori are fundamental examples of noncommutative spaces in operator algebras and noncommutative geometry, generalizing the algebra of functions on a classical torus by deforming the commutation relations of its coordinate functions.

Provenance (5 batches)

Stage Batch ID Job type Status
creating batch_69d6ab4669e48190b59246358b0383ab elicitation completed
NER batch_69d903f02638819091e0cc0e93fa5ea7 ner completed
NED1 batch_69f48b8111b88190a42a8904a2d26862 ned_source_triple completed
NED2 batch_69f495f069c48190a6e5856c272420c0 ned_description completed
NEDg batch_69f48fc7a8848190a06b34cc45db4789 nedg completed
Created at: April 8, 2026, 9:47 p.m.