Triple

T7705221
Position Surface form Disambiguated ID Type / Status
Subject Edgeworth expansion E174595 entity
Predicate isRelatedTo P37 FINISHED
Object Gram–Charlier series
The Gram–Charlier series is an asymptotic expansion that approximates a probability distribution by correcting a normal distribution using cumulants or moments to capture skewness and kurtosis.
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: Gram–Charlier series | Statement: [Edgeworth expansion, isRelatedTo, Gram–Charlier series]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gram–Charlier series
Context triple: [Edgeworth expansion, isRelatedTo, Gram–Charlier series]
  • A. 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.
  • B. Hermite
    Hermite is a French surname most famously associated with the 19th-century mathematician Charles Hermite, known for his contributions to number theory, algebra, and analysis.
  • C. Tukey's lambda distribution
    Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
  • D. Taylor series
    A Taylor series is an infinite sum of terms calculated from the derivatives of a function at a single point, used to represent and approximate functions as power series.
  • E. Bernoulli polynomials
    Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
  • 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: Gram–Charlier series
Triple: [Edgeworth expansion, isRelatedTo, Gram–Charlier series]
Generated description
The Gram–Charlier series is an asymptotic expansion that approximates a probability distribution by correcting a normal distribution using cumulants or moments to capture skewness and kurtosis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gram–Charlier series
Target entity description: The Gram–Charlier series is an asymptotic expansion that approximates a probability distribution by correcting a normal distribution using cumulants or moments to capture skewness and kurtosis.
  • A. Edgeworth expansion chosen
    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.
  • B. Hermite
    Hermite is a French surname most famously associated with the 19th-century mathematician Charles Hermite, known for his contributions to number theory, algebra, and analysis.
  • C. Tukey's lambda distribution
    Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
  • D. Taylor series
    A Taylor series is an infinite sum of terms calculated from the derivatives of a function at a single point, used to represent and approximate functions as power series.
  • E. Bernoulli polynomials
    Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
  • 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_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.