Triple
T1535800
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Berry–Esseen theorem |
E32545
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
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.
|
E174595
|
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: Edgeworth expansion | Statement: [Berry–Esseen theorem, relatedTo, Edgeworth expansion]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Edgeworth expansion Context triple: [Berry–Esseen theorem, relatedTo, Edgeworth expansion]
-
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.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
C.
Frisch–Waugh–Lovell theorem
The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
-
D.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
E.
Laplace law of error
The Laplace law of error is a probability distribution characterized by a sharp peak at the mean and heavier tails than the normal distribution, historically used to model the magnitude of observational errors.
- 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: Edgeworth expansion Triple: [Berry–Esseen theorem, relatedTo, Edgeworth expansion]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Edgeworth expansion Target entity description: 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.
-
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.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
C.
Frisch–Waugh–Lovell theorem
The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
-
D.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
E.
Laplace law of error
The Laplace law of error is a probability distribution characterized by a sharp peak at the mean and heavier tails than the normal distribution, historically used to model the magnitude of observational errors.
- 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_69a885ea86308190998f6bc14bb91f8e |
completed | March 4, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69a90829e60081909d3f9f79585e080e |
completed | March 5, 2026, 4:35 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ad295da0988190b1dc171bcdfe4d71 |
completed | March 8, 2026, 7:46 a.m. |
| NEDg | Description generation | batch_69ad29dc9fd08190b67527f0662c92dc |
completed | March 8, 2026, 7:48 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ad2a4d71a88190b67ed21beebbb479 |
completed | March 8, 2026, 7:50 a.m. |
Created at: March 4, 2026, 7:26 p.m.