Triple

T12095311
Position Surface form Disambiguated ID Type / Status
Subject Jacques Dixmier E288055 entity
Predicate notableConcept P201 FINISHED
Object Dixmier trace E962401 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: Dixmier trace | Statement: [Jacques Dixmier, notableConcept, Dixmier trace]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dixmier trace
Context triple: [Jacques Dixmier, notableConcept, Dixmier trace]
  • A. Dixmier trace chosen
    The Dixmier trace is a specialized non-normal trace used in functional analysis and noncommutative geometry to extend the notion of trace to certain unbounded operators.
  • B. Dixmier ideal
    A Dixmier ideal is a specific type of two-sided ideal in a C*-algebra that plays a key role in the structure and representation theory of operator algebras.
  • 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. Dixmier mapping in representation theory
    The Dixmier mapping in representation theory is a correspondence introduced by Jacques Dixmier that relates primitive ideals in the universal enveloping algebra of a Lie algebra to coadjoint orbits, playing a key role in understanding the orbit method and the structure of representations.
  • E. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • 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_69d6ab4964708190850585628b287b0c completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d91550ce508190babf5755e1553734 completed April 10, 2026, 3:20 p.m.
NED1 Entity disambiguation (via context triple) batch_69f60a6f22cc8190ba12c910c5ef5868 completed May 2, 2026, 2:30 p.m.
Created at: April 8, 2026, 9:48 p.m.