Triple

T22423417
Position Surface form Disambiguated ID Type / Status
Subject Erdős–Straus conjecture E554304 entity
Predicate relatedConcept P37 FINISHED
Object Egyptian fraction decomposition
Egyptian fraction decomposition is the representation of a rational number as a sum of distinct unit fractions, each with numerator 1.
E403440 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: Egyptian fraction decomposition | Statement: [Erdős–Straus conjecture, relatedConcept, Egyptian fraction decomposition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Egyptian fraction decomposition
Context triple: [Erdős–Straus conjecture, relatedConcept, Egyptian fraction decomposition]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Prouhet–Tarry–Escott problem
    The Prouhet–Tarry–Escott problem is a classic number theory problem that asks for distinct integer multisets whose powers up to a given degree have equal sums, making it a central example in the study of equal-sum power partitions and Diophantine equations.
  • E. Egyptian mathematics
    Egyptian mathematics is the body of mathematical knowledge and techniques developed in ancient Egypt, notable for its practical arithmetic, geometry, and use of unit fractions in administrative, architectural, and surveying applications.
  • 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: Egyptian fraction decomposition
Triple: [Erdős–Straus conjecture, relatedConcept, Egyptian fraction decomposition]
Generated description
Egyptian fraction decomposition is the representation of a rational number as a sum of distinct unit fractions, each with numerator 1.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Egyptian fraction decomposition
Target entity description: Egyptian fraction decomposition is the representation of a rational number as a sum of distinct unit fractions, each with numerator 1.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Prouhet–Tarry–Escott problem
    The Prouhet–Tarry–Escott problem is a classic number theory problem that asks for distinct integer multisets whose powers up to a given degree have equal sums, making it a central example in the study of equal-sum power partitions and Diophantine equations.
  • E. Egyptian mathematics chosen
    Egyptian mathematics is the body of mathematical knowledge and techniques developed in ancient Egypt, notable for its practical arithmetic, geometry, and use of unit fractions in administrative, architectural, and surveying applications.
  • F. None of above.

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_69e11e4f2d0c819091aa3558ea2ee630 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f15a2af620819083338127e78137dc completed April 29, 2026, 1:08 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0b0c66eaa88190a58d646620de8612 completed May 18, 2026, 12:56 p.m.
NEDg Description generation batch_6a0b0d8a6024819093541ef45e3a22b4 completed May 18, 2026, 1 p.m.
NED2 Entity disambiguation (via description) batch_6a0b0de37c208190ac16ec35b1a8edee completed May 18, 2026, 1:02 p.m.
Created at: April 16, 2026, 8:47 p.m.