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.