Triple
T1535807
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Berry–Esseen theorem |
E32545
|
entity |
| Predicate | hasGeneralizations |
P2372
|
FINISHED |
| Object | Berry–Esseen bounds for dependent variables |
E32545
|
NE FINISHED |
How this triple was built (2 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: Berry–Esseen bounds for dependent variables | Statement: [Berry–Esseen theorem, hasGeneralizations, Berry–Esseen bounds for dependent variables]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Berry–Esseen bounds for dependent variables Context triple: [Berry–Esseen theorem, hasGeneralizations, Berry–Esseen bounds for dependent variables]
-
A.
Berry–Esseen theorem
chosen
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.
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.
-
C.
Statistical Independence in Probability, Analysis and Number Theory
"Statistical Independence in Probability, Analysis and Number Theory" is a mathematical monograph by Mark Kac that explores the concept of independence across probability theory, real analysis, and number theory.
-
D.
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.
-
E.
Edgeworth expansion
Edgeworth expansion is an asymptotic series that refines the central limit theorem by providing higher-order approximations to the distribution of normalized sums of random variables.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69a885ea86308190998f6bc14bb91f8e |
completed | March 4, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69aa61dc6ab881908b22aa7a5295bf21 |
completed | March 6, 2026, 5:10 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ad30942dc481908de85bd2ca30c0bd |
completed | March 8, 2026, 8:17 a.m. |
Created at: March 4, 2026, 7:26 p.m.