Triple

T16151015
Position Surface form Disambiguated ID Type / Status
Subject families index theorem E391907 entity
Predicate influenced P9 FINISHED
Object Quillen’s superconnection formalism
Quillen’s superconnection formalism is a powerful geometric framework in differential geometry and global analysis that extends the notion of a connection to graded vector bundles, enabling elegant proofs and generalizations of index theorems for families of elliptic operators.
E1197991 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: Quillen’s superconnection formalism | Statement: [families index theorem, influenced, Quillen’s superconnection formalism]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Quillen’s superconnection formalism
Context triple: [families index theorem, influenced, Quillen’s superconnection formalism]
  • A. Chern–Simons forms
    Chern–Simons forms are secondary characteristic classes in differential geometry that arise from connections on principal bundles and play a central role in topological quantum field theories.
  • B. 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.
  • C. Chern–Weil theory
    Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
  • D. 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.
  • E. Cheeger–Simons differential characters
    Cheeger–Simons differential characters are geometric invariants that refine ordinary cohomology by incorporating both integral cohomology classes and differential form data, providing a model for differential cohomology theories.
  • 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: Quillen’s superconnection formalism
Triple: [families index theorem, influenced, Quillen’s superconnection formalism]
Generated description
Quillen’s superconnection formalism is a powerful geometric framework in differential geometry and global analysis that extends the notion of a connection to graded vector bundles, enabling elegant proofs and generalizations of index theorems for families of elliptic operators.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Quillen’s superconnection formalism
Target entity description: Quillen’s superconnection formalism is a powerful geometric framework in differential geometry and global analysis that extends the notion of a connection to graded vector bundles, enabling elegant proofs and generalizations of index theorems for families of elliptic operators.
  • A. Chern–Simons forms
    Chern–Simons forms are secondary characteristic classes in differential geometry that arise from connections on principal bundles and play a central role in topological quantum field theories.
  • B. 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.
  • C. Chern–Weil theory
    Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
  • D. 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.
  • E. Cheeger–Simons differential characters
    Cheeger–Simons differential characters are geometric invariants that refine ordinary cohomology by incorporating both integral cohomology classes and differential form data, providing a model for differential cohomology theories.
  • F. None of above. chosen

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_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_69fff7a9ebf08190aa21cdff051f4ba2 completed May 10, 2026, 3:12 a.m.
NEDg Description generation batch_69fff86a556c819096bc008e1ca76e8c completed May 10, 2026, 3:15 a.m.
NED2 Entity disambiguation (via description) batch_69fff926120081909f1042bf3a16ea10 completed May 10, 2026, 3:19 a.m.
Created at: April 10, 2026, 5:01 a.m.