Triple
T3677820
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Aleksandr Khinchin |
E78037
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
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.
|
E378993
|
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 law of the iterated logarithm | Statement: [Aleksandr Khinchin, notableWork, Khinchin's law of the iterated logarithm]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Khinchin's law of the iterated logarithm Context triple: [Aleksandr Khinchin, notableWork, Khinchin's law of the iterated logarithm]
-
A.
Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
-
B.
Kolmogorov zero–one law
The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
-
C.
Kakutani’s random ergodic theorem
Kakutani’s random ergodic theorem is a fundamental result in ergodic theory that extends classical ergodic theorems to sequences of randomly chosen measure-preserving transformations.
-
D.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
E.
Newcomb–Benford law
The Newcomb–Benford law is a statistical principle stating that in many naturally occurring datasets, the leading digits are distributed logarithmically, with smaller digits (especially 1) appearing as the first digit more frequently than larger ones.
- 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 law of the iterated logarithm Triple: [Aleksandr Khinchin, notableWork, Khinchin's law of the iterated logarithm]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Khinchin's law of the iterated logarithm Target entity description: 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.
-
A.
Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
-
B.
Kolmogorov zero–one law
The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
-
C.
Kakutani’s random ergodic theorem
Kakutani’s random ergodic theorem is a fundamental result in ergodic theory that extends classical ergodic theorems to sequences of randomly chosen measure-preserving transformations.
-
D.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
E.
Newcomb–Benford law
The Newcomb–Benford law is a statistical principle stating that in many naturally occurring datasets, the leading digits are distributed logarithmically, with smaller digits (especially 1) appearing as the first digit more frequently than larger ones.
- 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.