Triple

T3677837
Position Surface form Disambiguated ID Type / Status
Subject Aleksandr Khinchin E78037 entity
Predicate notableIdea P4 FINISHED
Object Khinchin's theorem on continued fractions
Khinchin's theorem on continued fractions is a fundamental result in metric number theory that describes the almost-everywhere behavior of the geometric mean of the partial quotients in the continued fraction expansions of real numbers, showing it converges to a universal constant now known as Khinchin's constant.
E378994 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: Khinchin's theorem on continued fractions | Statement: [Aleksandr Khinchin, notableIdea, Khinchin's theorem on continued fractions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Khinchin's theorem on continued fractions
Context triple: [Aleksandr Khinchin, notableIdea, Khinchin's theorem on continued fractions]
  • A. Khinchin's representation theorem
    Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
  • B. Khinchin's law of the iterated logarithm
    Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
  • C. Khinchin–Lévy constant
    The Khinchin–Lévy constant is a mathematical constant arising in metric number theory and continued fractions, describing the typical exponential growth rate of the denominators of convergents for almost all real numbers.
  • D. Khinchin's constant
    Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
  • E. 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.
  • 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: Khinchin's theorem on continued fractions
Triple: [Aleksandr Khinchin, notableIdea, Khinchin's theorem on continued fractions]
Generated description
Khinchin's theorem on continued fractions is a fundamental result in metric number theory that describes the almost-everywhere behavior of the geometric mean of the partial quotients in the continued fraction expansions of real numbers, showing it converges to a universal constant now known as Khinchin's constant.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Khinchin's theorem on continued fractions
Target entity description: Khinchin's theorem on continued fractions is a fundamental result in metric number theory that describes the almost-everywhere behavior of the geometric mean of the partial quotients in the continued fraction expansions of real numbers, showing it converges to a universal constant now known as Khinchin's constant.
  • A. Khinchin's representation theorem
    Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
  • B. Khinchin's law of the iterated logarithm
    Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
  • C. Khinchin–Lévy constant
    The Khinchin–Lévy constant is a mathematical constant arising in metric number theory and continued fractions, describing the typical exponential growth rate of the denominators of convergents for almost all real numbers.
  • D. Khinchin's constant chosen
    Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
  • E. 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.
  • 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_69ad85e18c1c8190be8aafb227f39f48 completed March 8, 2026, 2:21 p.m.
NER Named-entity recognition batch_69adc46599188190a046eddb0d85c483 completed March 8, 2026, 6:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69b4daffd6bc81908ac7a4b8b4073bc0 completed March 14, 2026, 3:50 a.m.
NEDg Description generation batch_69b4db9266f881908e31c7646b8c861c completed March 14, 2026, 3:52 a.m.
NED2 Entity disambiguation (via description) batch_69b4df53bb648190af6507919fd4d59d completed March 14, 2026, 4:08 a.m.
Created at: March 8, 2026, 3:25 p.m.