Triple

T3677821
Position Surface form Disambiguated ID Type / Status
Subject Aleksandr Khinchin E78037 entity
Predicate notableWork P4 FINISHED
Object 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.
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 constant | Statement: [Aleksandr Khinchin, notableWork, Khinchin's constant]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Khinchin's constant
Context triple: [Aleksandr Khinchin, notableWork, Khinchin's constant]
  • A. 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.
  • B. Kronecker’s lemma
    Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
  • C. 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.
  • D. Ulam sequence
    The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
  • E. Pi
    Pi is a 1998 psychological thriller film directed by Darren Aronofsky that explores obsession, mathematics, and mysticism through the story of a reclusive number theorist.
  • 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 constant
Triple: [Aleksandr Khinchin, notableWork, Khinchin's constant]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Khinchin's constant
Target entity description: 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.
  • A. 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.
  • B. Kronecker’s lemma
    Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
  • C. 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.
  • D. Ulam sequence
    The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
  • E. Pi
    Pi is a 1998 psychological thriller film directed by Darren Aronofsky that explores obsession, mathematics, and mysticism through the story of a reclusive number theorist.
  • 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.