Triple
T15502451
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Khinchin's law of the iterated logarithm |
E378993
|
entity |
| Predicate | isRelatedTo |
P37
|
FINISHED |
| Object |
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.
|
E1160946
|
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: Donsker's invariance principle | Statement: [Khinchin's law of the iterated logarithm, isRelatedTo, Donsker's invariance principle]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Donsker's invariance principle Context triple: [Khinchin's law of the iterated logarithm, isRelatedTo, Donsker's invariance principle]
-
A.
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.
-
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.
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.
-
D.
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.
-
E.
Lévy’s continuity theorem
Lévy’s continuity theorem is a fundamental result in probability theory that characterizes convergence in distribution of random variables via pointwise convergence of their characteristic functions.
- 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: Donsker's invariance principle Triple: [Khinchin's law of the iterated logarithm, isRelatedTo, Donsker's invariance principle]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Donsker's invariance principle Target entity description: 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.
-
A.
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.
-
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.
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.
-
D.
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.
-
E.
Lévy’s continuity theorem
Lévy’s continuity theorem is a fundamental result in probability theory that characterizes convergence in distribution of random variables via pointwise convergence of their characteristic functions.
- 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_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_69ff3669f908819087162b1b8a4e4320 |
completed | May 9, 2026, 1:28 p.m. |
| NEDg | Description generation | batch_69ff375856448190a61979dfff751f06 |
completed | May 9, 2026, 1:32 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69ff382f1bbc8190810d0d825430f9ea |
completed | May 9, 2026, 1:35 p.m. |
Created at: April 10, 2026, 3:54 a.m.