Triple
T4092334
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Khinchin–Kahane type inequalities |
E87730
|
entity |
| Predicate | generalizes |
P2372
|
FINISHED |
| Object |
Khinchin inequality
The Khinchin inequality is a fundamental result in probability theory and functional analysis that bounds the moments of sums of independent Rademacher (±1) random variables in terms of their ℓ² norm.
|
E87730
|
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: Khinchin inequality | Statement: [Khinchin–Kahane type inequalities, generalizes, Khinchin inequality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Khinchin inequality Context triple: [Khinchin–Kahane type inequalities, generalizes, Khinchin inequality]
-
A.
Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
-
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.
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.
-
D.
Khinchin's representation theorem
Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
-
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: Khinchin inequality Triple: [Khinchin–Kahane type inequalities, generalizes, Khinchin inequality]
Generated description
The Khinchin inequality is a fundamental result in probability theory and functional analysis that bounds the moments of sums of independent Rademacher (±1) random variables in terms of their ℓ² norm.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Khinchin inequality Target entity description: The Khinchin inequality is a fundamental result in probability theory and functional analysis that bounds the moments of sums of independent Rademacher (±1) random variables in terms of their ℓ² norm.
-
A.
Khinchin–Kahane type inequalities
chosen
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
-
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.
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.
-
D.
Khinchin's representation theorem
Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
-
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_69aed94425148190be337845d56fac22 |
completed | March 9, 2026, 2:29 p.m. |
| NER | Named-entity recognition | batch_69aefcae22a081908af65a960306b78c |
completed | March 9, 2026, 5 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b56b6cfb288190ac08c3a37327ac9a |
completed | March 14, 2026, 2:06 p.m. |
| NEDg | Description generation | batch_69b56cd11b5c8190b7e7c9c91b6564b6 |
completed | March 14, 2026, 2:12 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69b56d3ff45881909f8b2c21ce51e0f0 |
completed | March 14, 2026, 2:14 p.m. |
Created at: March 9, 2026, 3:40 p.m.