Triple
T7705167
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lindeberg–Feller central limit theorem |
E174594
|
entity |
| Predicate | generalizes |
P2372
|
FINISHED |
| Object |
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.
|
E683053
|
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: Lyapunov central limit theorem | Statement: [Lindeberg–Feller central limit theorem, generalizes, Lyapunov central limit theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lyapunov central limit theorem Context triple: [Lindeberg–Feller central limit theorem, generalizes, Lyapunov central limit theorem]
-
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.
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.
-
C.
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.
-
D.
Erdős–Rényi law of large numbers
The Erdős–Rényi law of large numbers is a refinement of the classical law of large numbers that provides precise asymptotic behavior and convergence rates for sums of independent random variables, developed by mathematicians Pál Erdős and Alfréd Rényi.
-
E.
Freidlin–Wentzell theory
Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
- 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: Lyapunov central limit theorem Triple: [Lindeberg–Feller central limit theorem, generalizes, Lyapunov central limit theorem]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Lyapunov central limit theorem Target entity description: 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.
-
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.
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.
-
C.
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.
-
D.
Erdős–Rényi law of large numbers
The Erdős–Rényi law of large numbers is a refinement of the classical law of large numbers that provides precise asymptotic behavior and convergence rates for sums of independent random variables, developed by mathematicians Pál Erdős and Alfréd Rényi.
-
E.
Freidlin–Wentzell theory
Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
- 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_69c6995b3e8c8190833108f883d5f53c |
completed | March 27, 2026, 2:51 p.m. |
| NER | Named-entity recognition | batch_69c7028f17f0819081686ac146750d3a |
completed | March 27, 2026, 10:19 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c8acc088148190ba5ba07e4ad2284c |
completed | March 29, 2026, 4:38 a.m. |
| NEDg | Description generation | batch_69c8ae313d4c8190964be233c0651f3a |
completed | March 29, 2026, 4:44 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c8aea55c0081909aa0f6c96c8d6a03 |
completed | March 29, 2026, 4:46 a.m. |
Created at: March 27, 2026, 4:03 p.m.