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.