Triple

T15502788
Position Surface form Disambiguated ID Type / Status
Subject Three Pearls of Number Theory E379002 entity
Predicate author P4 FINISHED
Object Martin Aigner
Martin Aigner was a German mathematician known for his work in combinatorics and number theory, as well as for authoring accessible and elegant mathematical texts.
 E1160955 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: Martin Aigner | Statement: [Three Pearls of Number Theory, author, Martin Aigner]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Martin Aigner
Context triple: [Three Pearls of Number Theory, author, Martin Aigner]
  • A. Ronald L. Graham
    Ronald L. Graham was an influential American mathematician known for his pioneering work in combinatorics, discrete mathematics, and computational geometry, as well as for popularizing mathematics through both research and expository writing.
  • B. Ronald Graham
    Ronald Graham was an American stage and film actor active in the early 20th century, known for his performances in musical theatre and Hollywood movies.
  • C. Gian-Carlo Rota
    Gian-Carlo Rota was an influential Italian-American mathematician and philosopher best known for his foundational work in combinatorics and probability, as well as his impactful essays on the philosophy of mathematics.
  • D. Richard K. Guy
    Richard K. Guy was a British-Canadian mathematician renowned for his work in number theory, combinatorics, and recreational mathematics, and for coauthoring influential books that popularized mathematical games and puzzles.
  • E. Emanuel Sperner
    Emanuel Sperner was a German mathematician known for his contributions to combinatorics and lattice theory, including the formulation of Sperner's lemma and Sperner's theorem.
  • 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: Martin Aigner
Triple: [Three Pearls of Number Theory, author, Martin Aigner]
Generated description
Martin Aigner was a German mathematician known for his work in combinatorics and number theory, as well as for authoring accessible and elegant mathematical texts.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Martin Aigner
Target entity description: Martin Aigner was a German mathematician known for his work in combinatorics and number theory, as well as for authoring accessible and elegant mathematical texts.
  • A. Ronald L. Graham
    Ronald L. Graham was an influential American mathematician known for his pioneering work in combinatorics, discrete mathematics, and computational geometry, as well as for popularizing mathematics through both research and expository writing.
  • B. Ronald Graham
    Ronald Graham was an American stage and film actor active in the early 20th century, known for his performances in musical theatre and Hollywood movies.
  • C. Gian-Carlo Rota
    Gian-Carlo Rota was an influential Italian-American mathematician and philosopher best known for his foundational work in combinatorics and probability, as well as his impactful essays on the philosophy of mathematics.
  • D. Richard K. Guy
    Richard K. Guy was a British-Canadian mathematician renowned for his work in number theory, combinatorics, and recreational mathematics, and for coauthoring influential books that popularized mathematical games and puzzles.
  • E. Emanuel Sperner
    Emanuel Sperner was a German mathematician known for his contributions to combinatorics and lattice theory, including the formulation of Sperner's lemma and Sperner's theorem.
  • 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_69d85cd53a7c819080f5b9042c4c199e completed April 10, 2026, 2:13 a.m.
NER Named-entity recognition batch_69e03fcc5bb88190b8a9a81419a9a38b completed April 16, 2026, 1:47 a.m.
NED1 Entity disambiguation (via context triple) batch_69ff3669f908819087162b1b8a4e4320 completed May 9, 2026, 1:28 p.m.
NEDg Description generation batch_69ff375856448190a61979dfff751f06 completed May 9, 2026, 1:32 p.m.
NED2 Entity disambiguation (via description) batch_69ff382f1bbc8190810d0d825430f9ea completed May 9, 2026, 1:35 p.m.
Created at: April 10, 2026, 3:54 a.m.