Triple

T1531402
Position Surface form Disambiguated ID Type / Status
Subject Concrete Mathematics E32450 entity
Predicate author P4 FINISHED
Object 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.
E205446 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: Ronald L. Graham | Statement: [Concrete Mathematics, author, Ronald L. Graham]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ronald L. Graham
Context triple: [Concrete Mathematics, author, Ronald L. Graham]
  • A. 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.
  • B. Elwyn R. Berlekamp
    Elwyn R. Berlekamp was an American mathematician and engineer known for his influential work in coding theory, combinatorial game theory, and algorithms.
  • 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 Lipton
    Richard Lipton is an American computer scientist known for his influential work in theoretical computer science and cryptography, including contributions to complexity theory and algorithm design.
  • E. Murray Klamkin
    Murray Klamkin was a prominent American mathematician and problem solver known for his influential work in mathematical problem posing, editing, and education.
  • 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: Ronald L. Graham
Triple: [Concrete Mathematics, author, Ronald L. Graham]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Ronald L. Graham
Target entity description: 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.
  • A. 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.
  • B. Elwyn R. Berlekamp
    Elwyn R. Berlekamp was an American mathematician and engineer known for his influential work in coding theory, combinatorial game theory, and algorithms.
  • 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 Lipton
    Richard Lipton is an American computer scientist known for his influential work in theoretical computer science and cryptography, including contributions to complexity theory and algorithm design.
  • E. Murray Klamkin
    Murray Klamkin was a prominent American mathematician and problem solver known for his influential work in mathematical problem posing, editing, and education.
  • 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_69a885ea86308190998f6bc14bb91f8e completed March 4, 2026, 7:20 p.m.
NER Named-entity recognition batch_69a90816b5e88190aa92a8558e35744b completed March 5, 2026, 4:35 a.m.
NED1 Entity disambiguation (via context triple) batch_69adc98b2b0081909d10b22d59c5e653 completed March 8, 2026, 7:10 p.m.
NEDg Description generation batch_69adcaed1f788190b14c3e2d2c3036d9 completed March 8, 2026, 7:15 p.m.
NED2 Entity disambiguation (via description) batch_69adcbee97e88190adc1315c0a5013ab completed March 8, 2026, 7:20 p.m.
Created at: March 4, 2026, 7:26 p.m.