Triple

T2652955
Position Surface form Disambiguated ID Type / Status
Subject Whitney approximation theorem E53941 entity
Predicate standardReference P33736 FINISHED
Object M. Hirsch, Differential Topology
*Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
 E285920 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: M. Hirsch, Differential Topology | Statement: [Whitney approximation theorem, standardReference, M. Hirsch, Differential Topology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: M. Hirsch, Differential Topology
Context triple: [Whitney approximation theorem, standardReference, M. Hirsch, Differential Topology]
  • A. Stephen Smale
    Stephen Smale is an American mathematician renowned for his work in topology, dynamical systems, and mathematical economics, and as a recipient of the Fields Medal.
  • B. René Thom
    René Thom was a French mathematician renowned for developing catastrophe theory and making fundamental contributions to topology, for which he received the Fields Medal.
  • C. 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.
  • D. Dusa McDuff
    Dusa McDuff is a prominent British-American mathematician renowned for her foundational contributions to symplectic geometry and topology.
  • E. 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.
  • 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: M. Hirsch, Differential Topology
Triple: [Whitney approximation theorem, standardReference, M. Hirsch, Differential Topology]
Generated description
*Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: M. Hirsch, Differential Topology
Target entity description: *Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
  • A. Stephen Smale
    Stephen Smale is an American mathematician renowned for his work in topology, dynamical systems, and mathematical economics, and as a recipient of the Fields Medal.
  • B. René Thom
    René Thom was a French mathematician renowned for developing catastrophe theory and making fundamental contributions to topology, for which he received the Fields Medal.
  • C. 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.
  • D. Dusa McDuff
    Dusa McDuff is a prominent British-American mathematician renowned for her foundational contributions to symplectic geometry and topology.
  • E. 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.
  • 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_69ab495e192081909c77b622e8e7e15a completed March 6, 2026, 9:38 p.m.
NER Named-entity recognition batch_69abd93197f48190b04faf358b503204 completed March 7, 2026, 7:52 a.m.
NED1 Entity disambiguation (via context triple) batch_69af98ce81fc8190b7c6c66acfcb87c7 completed March 10, 2026, 4:06 a.m.
NEDg Description generation batch_69af99416924819099d4acb1a2d60e0c completed March 10, 2026, 4:08 a.m.
NED2 Entity disambiguation (via description) batch_69af99adadb08190a44f2286b25bf0aa completed March 10, 2026, 4:10 a.m.
Created at: March 6, 2026, 9:53 p.m.