Triple

T22964765
Position Surface form Disambiguated ID Type / Status
Subject Sylvester sequence E571006 entity
Predicate relatedTo P37 FINISHED
Object Egyptian fraction greedy algorithm — NE NERFINISHED

How this triple was built (3 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: Egyptian fraction greedy algorithm | Statement: [Sylvester sequence, relatedTo, Egyptian fraction greedy algorithm]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Egyptian fraction greedy algorithm
Context triple: [Sylvester sequence, relatedTo, Egyptian fraction greedy algorithm]
  • A. Farey sequence
    The Farey sequence is an ordered list of completely reduced fractions between 0 and 1 with denominators up to a given integer, widely studied in number theory for its connections to fractions, mediants, and modular forms.
  • B. Erdős–Straus conjecture
    The Erdős–Straus conjecture is an unsolved problem in number theory asserting that for every integer n ≥ 2, the fraction 4/n can be expressed as a sum of three unit fractions.
  • C. Continued Fractions
    Continued Fractions is a classic mathematical monograph by Aleksandr Khinchin that systematically develops the theory and applications of continued fraction expansions in number theory and analysis.
  • D. Stern–Brocot tree
    The Stern–Brocot tree is an infinite binary tree that systematically lists all positive rational numbers in lowest terms exactly once, ordered by increasing value.
  • E. Zeckendorf
    Zeckendorf is a surname most notably associated with American real estate developer William Zeckendorf and his influential role in mid-20th-century urban development.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Egyptian fraction greedy algorithm
Target entity description: The Egyptian fraction greedy algorithm is a method for expressing any positive rational number as a sum of distinct unit fractions by repeatedly subtracting the largest possible unit fraction at each step.
  • A. Farey sequence
    The Farey sequence is an ordered list of completely reduced fractions between 0 and 1 with denominators up to a given integer, widely studied in number theory for its connections to fractions, mediants, and modular forms.
  • B. Erdős–Straus conjecture
    The Erdős–Straus conjecture is an unsolved problem in number theory asserting that for every integer n ≥ 2, the fraction 4/n can be expressed as a sum of three unit fractions.
  • C. Continued Fractions
    Continued Fractions is a classic mathematical monograph by Aleksandr Khinchin that systematically develops the theory and applications of continued fraction expansions in number theory and analysis.
  • D. Stern–Brocot tree
    The Stern–Brocot tree is an infinite binary tree that systematically lists all positive rational numbers in lowest terms exactly once, ordered by increasing value.
  • E. Zeckendorf
    Zeckendorf is a surname most notably associated with American real estate developer William Zeckendorf and his influential role in mid-20th-century urban development.
  • F. None of above. chosen

Provenance (2 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_69e245b212a88190b5259caf51606084 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f181f763688190aab8f444a1a71577 completed April 29, 2026, 3:58 a.m.
Created at: April 17, 2026, 3:47 p.m.