Triple

T429524
Position Surface form Disambiguated ID Type / Status
Subject Whitney embedding theorem E9682 entity
Predicate namedAfter P63 FINISHED
Object Hassler Whitney
Hassler Whitney was an influential American mathematician known for foundational contributions to differential topology and geometry, including work on manifolds, embeddings, and singularities.
E53940 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: Hassler Whitney | Statement: [Whitney embedding theorem, namedAfter, Hassler Whitney]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hassler Whitney
Context triple: [Whitney embedding theorem, namedAfter, Hassler Whitney]
  • A. John Milnor
    John Milnor is an American mathematician renowned for his groundbreaking work in differential topology, K-theory, and dynamical systems, and is one of the most influential figures in modern mathematics.
  • B. Saunders Mac Lane
    Saunders Mac Lane was an American mathematician best known as a co-founder of category theory and for his influential work in algebra and homological algebra.
  • C. Max Dehn
    Max Dehn was a German mathematician known for his foundational work in topology and group theory, including the introduction of Dehn surgery and the study of decision problems in group theory.
  • D. Isadore Singer
    Isadore Singer was an American mathematician renowned for co-formulating the Atiyah–Singer Index Theorem, a foundational result linking analysis, topology, and geometry.
  • E. Shiing-Shen Chern
    Shiing-Shen Chern was a Chinese-American mathematician renowned for his foundational contributions to differential geometry and the development of Chern classes in topology.
  • 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: Hassler Whitney
Triple: [Whitney embedding theorem, namedAfter, Hassler Whitney]
Generated description
Hassler Whitney was an influential American mathematician known for foundational contributions to differential topology and geometry, including work on manifolds, embeddings, and singularities.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hassler Whitney
Target entity description: Hassler Whitney was an influential American mathematician known for foundational contributions to differential topology and geometry, including work on manifolds, embeddings, and singularities.
  • A. John Milnor
    John Milnor is an American mathematician renowned for his groundbreaking work in differential topology, K-theory, and dynamical systems, and is one of the most influential figures in modern mathematics.
  • B. Saunders Mac Lane
    Saunders Mac Lane was an American mathematician best known as a co-founder of category theory and for his influential work in algebra and homological algebra.
  • C. Max Dehn
    Max Dehn was a German mathematician known for his foundational work in topology and group theory, including the introduction of Dehn surgery and the study of decision problems in group theory.
  • D. Isadore Singer
    Isadore Singer was an American mathematician renowned for co-formulating the Atiyah–Singer Index Theorem, a foundational result linking analysis, topology, and geometry.
  • E. Shiing-Shen Chern
    Shiing-Shen Chern was a Chinese-American mathematician renowned for his foundational contributions to differential geometry and the development of Chern classes in topology.
  • 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_69a2e801e1d48190b505d1dd336b52ac completed Feb. 28, 2026, 1:05 p.m.
NER Named-entity recognition batch_69a2eeedf68c81908473d6c6600961bd completed Feb. 28, 2026, 1:34 p.m.
NED1 Entity disambiguation (via context triple) batch_69a42f67dc3881908d4b1c2f1fbc2aaa completed March 1, 2026, 12:22 p.m.
NEDg Description generation batch_69a42fdc1edc81908a8c0b82482a9af2 completed March 1, 2026, 12:23 p.m.
NED2 Entity disambiguation (via description) batch_69a4304138bc81909e524ff2567b82b3 completed March 1, 2026, 12:25 p.m.
Created at: Feb. 28, 2026, 1:11 p.m.