Triple

T8657097
Position Surface form Disambiguated ID Type / Status
Subject Ronald L. Graham E205446 entity
Predicate knownFor P22 FINISHED
Object Graham's number
Graham's number is an extraordinarily large number that arose in a problem in Ramsey theory and became famous as one of the largest numbers ever used in a serious mathematical proof.
E748745 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: Graham's number | Statement: [Ronald L. Graham, knownFor, Graham's number]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Graham's number
Context triple: [Ronald L. Graham, knownFor, Graham's number]
  • A. Conway chained arrow notation
    Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
  • B. Numberwang
    Numberwang is a surreal, fast-paced parody of television quiz shows from the British comedy duo Mitchell and Webb, known for its nonsensical rules and absurd humor.
  • C. Ackermann function
    The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
  • D. Feferman–Schütte ordinal
    The Feferman–Schütte ordinal is a large countable ordinal that marks the proof-theoretic strength of predicative arithmetic and analysis, serving as a key boundary in ordinal analysis and foundations of mathematics.
  • E. Knuth’s up-arrow notation
    Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
  • 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: Graham's number
Triple: [Ronald L. Graham, knownFor, Graham's number]
Generated description
Graham's number is an extraordinarily large number that arose in a problem in Ramsey theory and became famous as one of the largest numbers ever used in a serious mathematical proof.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Graham's number
Target entity description: Graham's number is an extraordinarily large number that arose in a problem in Ramsey theory and became famous as one of the largest numbers ever used in a serious mathematical proof.
  • A. Conway chained arrow notation
    Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
  • B. Numberwang
    Numberwang is a surreal, fast-paced parody of television quiz shows from the British comedy duo Mitchell and Webb, known for its nonsensical rules and absurd humor.
  • C. Ackermann function
    The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
  • D. Feferman–Schütte ordinal
    The Feferman–Schütte ordinal is a large countable ordinal that marks the proof-theoretic strength of predicative arithmetic and analysis, serving as a key boundary in ordinal analysis and foundations of mathematics.
  • E. Knuth’s up-arrow notation
    Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
  • 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_69ca8350897c819086cde7596fbe5fe7 completed March 30, 2026, 2:06 p.m.
NER Named-entity recognition batch_69cc484569788190aa41395854684e6f completed March 31, 2026, 10:18 p.m.
NED1 Entity disambiguation (via context triple) batch_69ceccec941881908263cd3205f10ccd completed April 2, 2026, 8:09 p.m.
NEDg Description generation batch_69cece8c4bdc8190988990c675f50f86 completed April 2, 2026, 8:16 p.m.
NED2 Entity disambiguation (via description) batch_69cecf3a0e78819082cc7c43eceae309 completed April 2, 2026, 8:19 p.m.
Created at: March 30, 2026, 6:30 p.m.