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.