Triple
T3677829
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Aleksandr Khinchin |
E78037
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Limit Laws for Sums of Independent Random Variables
Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
|
E379000
|
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: Limit Laws for Sums of Independent Random Variables | Statement: [Aleksandr Khinchin, notableWork, Limit Laws for Sums of Independent Random Variables]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Limit Laws for Sums of Independent Random Variables Context triple: [Aleksandr Khinchin, notableWork, Limit Laws for Sums of Independent Random Variables]
-
A.
Lindeberg–Feller central limit theorem
The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
-
B.
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.
-
C.
Isserlis’ theorem in probability theory
Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
-
D.
Modern Probability Theory and Its Applications
"Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
-
E.
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.
- 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: Limit Laws for Sums of Independent Random Variables Triple: [Aleksandr Khinchin, notableWork, Limit Laws for Sums of Independent Random Variables]
Generated description
Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Limit Laws for Sums of Independent Random Variables Target entity description: Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
-
A.
Lindeberg–Feller central limit theorem
The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
-
B.
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.
-
C.
Isserlis’ theorem in probability theory
Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
-
D.
Modern Probability Theory and Its Applications
"Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
-
E.
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.
- 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.