Triple
T3821387
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Atiyah–Singer index theorem |
E84379
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object |
Chern character
The Chern character is a fundamental homomorphism from K-theory to cohomology that translates vector bundles into characteristic classes, playing a central role in index theory and algebraic topology.
|
E391904
|
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: Chern character | Statement: [Atiyah–Singer index theorem, usesConcept, Chern character]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Chern character Context triple: [Atiyah–Singer index theorem, usesConcept, Chern character]
-
A.
Chern classes
Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
-
B.
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.
-
C.
Characteristic Classes
Characteristic Classes is a foundational mathematical text in differential topology and geometry that systematically develops the theory of characteristic classes for vector bundles and fiber bundles.
-
D.
Hirzebruch–Riemann–Roch theorem
The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
-
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. 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: Chern character Triple: [Atiyah–Singer index theorem, usesConcept, Chern character]
Generated description
The Chern character is a fundamental homomorphism from K-theory to cohomology that translates vector bundles into characteristic classes, playing a central role in index theory and algebraic topology.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Chern character Target entity description: The Chern character is a fundamental homomorphism from K-theory to cohomology that translates vector bundles into characteristic classes, playing a central role in index theory and algebraic topology.
-
A.
Chern classes
Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
-
B.
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.
-
C.
Characteristic Classes
Characteristic Classes is a foundational mathematical text in differential topology and geometry that systematically develops the theory of characteristic classes for vector bundles and fiber bundles.
-
D.
Hirzebruch–Riemann–Roch theorem
The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
-
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. 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_69aed931f5908190be2c07af66d4df25 |
completed | March 9, 2026, 2:29 p.m. |
| NER | Named-entity recognition | batch_69aeea62cdfc81909a3bf458b73d60e7 |
completed | March 9, 2026, 3:42 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b4fb4998248190b4174dd80a8e790c |
completed | March 14, 2026, 6:08 a.m. |
| NEDg | Description generation | batch_69b4ffcf7e24819098cf2e46b92bed4a |
completed | March 14, 2026, 6:27 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69b500596e308190a31e44c24de3f31d |
completed | March 14, 2026, 6:29 a.m. |
Created at: March 9, 2026, 3:17 p.m.