Triple

T3821388
Position Surface form Disambiguated ID Type / Status
Subject Atiyah–Singer index theorem E84379 entity
Predicate usesConcept P531 FINISHED
Object Todd class
The Todd class is a characteristic class in complex geometry and topology that plays a central role in index theorems by encoding curvature information of complex vector bundles.
 E391905 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: Todd class | Statement: [Atiyah–Singer index theorem, usesConcept, Todd class]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Todd class
Context triple: [Atiyah–Singer index theorem, usesConcept, Todd class]
  • A. Y class
    Y class is the standard economy fare class used by airlines, typically representing full-fare economy tickets with the least restrictions on changes and refunds.
  • B. Klas
    Klas is a Scandinavian given name, commonly used as a variant of Nicholas.
  • C. Tucker
    Tucker is a surname most notably associated with Albert W. Tucker, a Canadian-American mathematician and game theorist known for his contributions to topology and the formalization of the prisoner's dilemma.
  • D. Schull
    Schull is a small coastal village and popular tourist destination on the Mizen Peninsula in West County Cork, Ireland.
  • E. Tri-C
    Tri-C is a large public community college in Cuyahoga County, Ohio, offering a wide range of associate degrees, certificates, and workforce training programs.
  • 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: Todd class
Triple: [Atiyah–Singer index theorem, usesConcept, Todd class]
Generated description
The Todd class is a characteristic class in complex geometry and topology that plays a central role in index theorems by encoding curvature information of complex vector bundles.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Todd class
Target entity description: The Todd class is a characteristic class in complex geometry and topology that plays a central role in index theorems by encoding curvature information of complex vector bundles.
  • A. Y class
    Y class is the standard economy fare class used by airlines, typically representing full-fare economy tickets with the least restrictions on changes and refunds.
  • B. Klas
    Klas is a Scandinavian given name, commonly used as a variant of Nicholas.
  • C. Tucker
    Tucker is a surname most notably associated with Albert W. Tucker, a Canadian-American mathematician and game theorist known for his contributions to topology and the formalization of the prisoner's dilemma.
  • D. Schull
    Schull is a small coastal village and popular tourist destination on the Mizen Peninsula in West County Cork, Ireland.
  • E. Tri-C
    Tri-C is a large public community college in Cuyahoga County, Ohio, offering a wide range of associate degrees, certificates, and workforce training programs.
  • 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.