Triple

T3677830
Position Surface form Disambiguated ID Type / Status
Subject Aleksandr Khinchin E78037 entity
Predicate notableWork P4 FINISHED
Object 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.
E379001 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: Continued Fractions | Statement: [Aleksandr Khinchin, notableWork, Continued Fractions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Continued Fractions
Context triple: [Aleksandr Khinchin, notableWork, Continued Fractions]
  • A. Farey tessellation
    The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
  • B. Diophantine approximation
    Diophantine approximation is a branch of number theory that studies how closely real numbers can be approximated by rational numbers, often with quantitative bounds on the quality of approximation.
  • C. Lucas sequences
    Lucas sequences are a family of integer sequences defined by the same type of second-order linear recurrence as the Fibonacci numbers but with more general initial conditions, encompassing the Fibonacci sequence as a special case.
  • D. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • E. Ramanujan’s sum
    Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
  • 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: Continued Fractions
Triple: [Aleksandr Khinchin, notableWork, Continued Fractions]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Continued Fractions
Target entity description: 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.
  • A. Farey tessellation
    The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
  • B. Diophantine approximation
    Diophantine approximation is a branch of number theory that studies how closely real numbers can be approximated by rational numbers, often with quantitative bounds on the quality of approximation.
  • C. Lucas sequences
    Lucas sequences are a family of integer sequences defined by the same type of second-order linear recurrence as the Fibonacci numbers but with more general initial conditions, encompassing the Fibonacci sequence as a special case.
  • D. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • E. Ramanujan’s sum
    Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
  • 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_69ad85e18c1c8190be8aafb227f39f48 completed March 8, 2026, 2:21 p.m.
NER Named-entity recognition batch_69adc4643cf08190b2d10ddf4aac7407 completed March 8, 2026, 6:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69b4c3a50d40819081aad0c72bcaee9d completed March 14, 2026, 2:10 a.m.
NEDg Description generation batch_69b4c451a5048190bfd4675cd17de655 completed March 14, 2026, 2:13 a.m.
NED2 Entity disambiguation (via description) batch_69b4c494ad80819084d6aa10fe62a63b completed March 14, 2026, 2:14 a.m.
Created at: March 8, 2026, 3:25 p.m.