Triple
T15502523
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Khinchin–Kolmogorov theorem |
E378995
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Kolmogorov three-series theorem
The Kolmogorov three-series theorem is a fundamental result in probability theory that gives necessary and sufficient conditions for the almost sure convergence of a series of independent random variables.
|
E378995
|
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: Kolmogorov three-series theorem | Statement: [Khinchin–Kolmogorov theorem, relatedTo, Kolmogorov three-series theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kolmogorov three-series theorem Context triple: [Khinchin–Kolmogorov theorem, relatedTo, Kolmogorov three-series theorem]
-
A.
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.
-
B.
Khinchin–Kolmogorov theorem
The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
-
C.
Borel–Cantelli lemmas
The Borel–Cantelli lemmas are fundamental results in probability theory that characterize when events occur infinitely often or only finitely often, based on the convergence or divergence of the sum of their probabilities.
-
D.
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.
-
E.
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.
- 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: Kolmogorov three-series theorem Triple: [Khinchin–Kolmogorov theorem, relatedTo, Kolmogorov three-series theorem]
Generated description
The Kolmogorov three-series theorem is a fundamental result in probability theory that gives necessary and sufficient conditions for the almost sure convergence of a series of independent random variables.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kolmogorov three-series theorem Target entity description: The Kolmogorov three-series theorem is a fundamental result in probability theory that gives necessary and sufficient conditions for the almost sure convergence of a series of independent random variables.
-
A.
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.
-
B.
Khinchin–Kolmogorov theorem
chosen
The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
-
C.
Borel–Cantelli lemmas
The Borel–Cantelli lemmas are fundamental results in probability theory that characterize when events occur infinitely often or only finitely often, based on the convergence or divergence of the sum of their probabilities.
-
D.
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.
-
E.
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.
- 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_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_69ff3830f0148190846bd24db1e0d754 |
completed | May 9, 2026, 1:35 p.m. |
Created at: April 10, 2026, 3:54 a.m.