Triple
T15502449
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Khinchin's law of the iterated logarithm |
E378993
|
entity |
| Predicate | isRelatedTo |
P37
|
FINISHED |
| Object |
Hartman–Wintner law of the iterated logarithm
The Hartman–Wintner law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuation magnitude of partial sums of independent random variables, refining the classical central limit theorem.
|
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: Hartman–Wintner law of the iterated logarithm | Statement: [Khinchin's law of the iterated logarithm, isRelatedTo, Hartman–Wintner law of the iterated logarithm]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hartman–Wintner law of the iterated logarithm Context triple: [Khinchin's law of the iterated logarithm, isRelatedTo, Hartman–Wintner law of the iterated logarithm]
-
A.
Kolmogorov's law of the iterated logarithm
Kolmogorov'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 between the law of large numbers and the central limit theorem.
-
B.
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.
-
C.
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.
-
D.
Lyapunov central limit theorem
The Lyapunov central limit theorem is a version of the central limit theorem that provides sufficient moment conditions under which the normalized sum of independent (not necessarily identically distributed) random variables converges in distribution to a normal law.
-
E.
Donsker's invariance principle
Donsker's invariance principle is a fundamental result in probability theory stating that suitably normalized random walks converge in distribution to Brownian motion, providing a functional central limit theorem.
- 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: Hartman–Wintner law of the iterated logarithm Triple: [Khinchin's law of the iterated logarithm, isRelatedTo, Hartman–Wintner law of the iterated logarithm]
Generated description
The Hartman–Wintner law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuation magnitude of partial sums of independent random variables, refining the classical central limit theorem.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hartman–Wintner law of the iterated logarithm Target entity description: The Hartman–Wintner law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuation magnitude of partial sums of independent random variables, refining the classical central limit theorem.
-
A.
Kolmogorov's law of the iterated logarithm
Kolmogorov'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 between the law of large numbers and the central limit theorem.
-
B.
Khinchin's law of the iterated logarithm
chosen
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.
-
C.
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.
-
D.
Lyapunov central limit theorem
The Lyapunov central limit theorem is a version of the central limit theorem that provides sufficient moment conditions under which the normalized sum of independent (not necessarily identically distributed) random variables converges in distribution to a normal law.
-
E.
Donsker's invariance principle
Donsker's invariance principle is a fundamental result in probability theory stating that suitably normalized random walks converge in distribution to Brownian motion, providing a functional central limit theorem.
- F. None of above.
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_69d85cd53a7c819080f5b9042c4c199e |
completed | April 10, 2026, 2:13 a.m. |
| NER | Named-entity recognition | batch_69e03fcc5bb88190b8a9a81419a9a38b |
completed | April 16, 2026, 1:47 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ff4c345f888190be7a684f3bd86324 |
completed | May 9, 2026, 3:01 p.m. |
| NEDg | Description generation | batch_69ff4d4dd8108190aa3271a9feaea5ca |
completed | May 9, 2026, 3:05 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69ff4e29e8a48190bf7728cf2d099a7e |
completed | May 9, 2026, 3:09 p.m. |
Created at: April 10, 2026, 3:54 a.m.