Triple

T12027021
Position Surface form Disambiguated ID Type / Status
Subject Noncommutative Geometry (1994 book) E286303 entity
Predicate subject P450 FINISHED
Object Dirac operators E391906 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: Dirac operators | Statement: [Noncommutative Geometry (1994 book), subject, Dirac operators]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirac operators
Context triple: [Noncommutative Geometry (1994 book), subject, Dirac operators]
  • A. Dirac operator chosen
    The Dirac operator is a fundamental first-order differential operator on spinor fields that generalizes the classical Dirac equation and plays a central role in geometry, topology, and quantum field theory.
  • B. Schrödinger operators
    Schrödinger operators are a class of differential operators fundamental in quantum mechanics and spectral theory, used to describe the energy and dynamics of quantum systems.
  • C. Fredholm modules
    Fredholm modules are algebraic-analytic structures in noncommutative geometry that generalize elliptic operators and encode K-homology classes for C*-algebras.
  • D. equivariant index theorem
    The equivariant index theorem is a generalization of the Atiyah–Singer index theorem that computes indices of elliptic operators while taking into account the action of a symmetry group.
  • E. Atiyah–Singer index theorem
    The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
  • 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_69f49d4f4c80819082ffc0c5aa3505a0 completed May 1, 2026, 12:32 p.m.
Created at: April 8, 2026, 9:47 p.m.