Triple

T10269859
Position Surface form Disambiguated ID Type / Status
Subject Chern–Simons theory E240804 entity
Predicate hasMathematicalOriginIn P48732 FINISHED
Object 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.
E856766 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–Simons forms | Statement: [Chern–Simons theory, hasMathematicalOriginIn, Chern–Simons forms]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Chern–Simons forms
Context triple: [Chern–Simons theory, hasMathematicalOriginIn, Chern–Simons forms]
  • A. Chern–Simons theory
    Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
  • 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. 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.
  • 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. Pontryagin classes
    Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential 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–Simons forms
Triple: [Chern–Simons theory, hasMathematicalOriginIn, Chern–Simons forms]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Chern–Simons forms
Target entity description: 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.
  • A. Chern–Simons theory
    Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
  • 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. 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.
  • 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. Pontryagin classes
    Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential 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_69d381a94c1881908fc38fc263d9b9c2 completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4dfbfa26c8190b536655d33112ddf completed April 7, 2026, 10:43 a.m.
NED1 Entity disambiguation (via context triple) batch_69d74ff95bd08190975bc98c681caf07 completed April 9, 2026, 7:06 a.m.
NEDg Description generation batch_69d751122d208190abaa4fd72a07643b completed April 9, 2026, 7:11 a.m.
NED2 Entity disambiguation (via description) batch_69d751d4aa908190a825322ebf0066af completed April 9, 2026, 7:14 a.m.
Created at: April 6, 2026, 11:35 a.m.