Triple

T16151019
Position Surface form Disambiguated ID Type / Status
Subject families index theorem E391907 entity
Predicate relatedTo P37 FINISHED
Object Atiyah–Singer index theorem for a single operator E84379 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: Atiyah–Singer index theorem for a single operator | Statement: [families index theorem, relatedTo, Atiyah–Singer index theorem for a single operator]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Atiyah–Singer index theorem for a single operator
Context triple: [families index theorem, relatedTo, Atiyah–Singer index theorem for a single operator]
  • A. Atiyah–Singer index theorem chosen
    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.
  • B. Bismut’s local families index theorem
    Bismut’s local families index theorem is a refinement of the Atiyah–Singer families index theorem that expresses the family index in terms of local differential-geometric data using superconnection techniques.
  • C. Atiyah–Bott fixed-point theorem
    The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
  • D. 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.
  • E. 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.
  • 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_69d87f1c65e48190aa2b4c472e9bafc4 completed April 10, 2026, 4:39 a.m.
NER Named-entity recognition batch_69e21d9724808190a8332987583a345a completed April 17, 2026, 11:46 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0017a45620819098ab5fa50e73e7a9 completed May 10, 2026, 5:29 a.m.
Created at: April 10, 2026, 5:01 a.m.