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.