Triple

T6327847
Position Surface form Disambiguated ID Type / Status
Subject enumerative combinatorics E141901 entity
Predicate usesConcept P531 FINISHED
Object Bell numbers
Bell numbers are a sequence in combinatorics that count the number of ways to partition a finite set into nonempty, unlabeled subsets.
E586577 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: Bell numbers | Statement: [enumerative combinatorics, usesConcept, Bell numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bell numbers
Context triple: [enumerative combinatorics, usesConcept, Bell numbers]
  • A. The Twelvefold Way
    The Twelvefold Way is a framework in combinatorics that systematically classifies twelve fundamental ways of counting functions between finite sets under various labeling and structural constraints.
  • B. Delannoy
    Delannoy is a French surname, often associated with historical figures and families of French or Flemish origin.
  • C. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • D. Pascal's triangle
    Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
  • E. Pochhammer symbol
    The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
  • 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: Bell numbers
Triple: [enumerative combinatorics, usesConcept, Bell numbers]
Generated description
Bell numbers are a sequence in combinatorics that count the number of ways to partition a finite set into nonempty, unlabeled subsets.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bell numbers
Target entity description: Bell numbers are a sequence in combinatorics that count the number of ways to partition a finite set into nonempty, unlabeled subsets.
  • A. The Twelvefold Way
    The Twelvefold Way is a framework in combinatorics that systematically classifies twelve fundamental ways of counting functions between finite sets under various labeling and structural constraints.
  • B. Delannoy
    Delannoy is a French surname, often associated with historical figures and families of French or Flemish origin.
  • C. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • D. Pascal's triangle
    Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
  • E. Pochhammer symbol
    The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
  • 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_69c008d201748190917e69c41ba3f978 completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c064e9532081908277f10ec380a486 completed March 22, 2026, 9:53 p.m.
NED1 Entity disambiguation (via context triple) batch_69c60410223081908c1cf3663d4b14c0 completed March 27, 2026, 4:14 a.m.
NEDg Description generation batch_69c60626724881908e6270c2d3652c16 completed March 27, 2026, 4:23 a.m.
NED2 Entity disambiguation (via description) batch_69c606bd2228819082fcb63493664927 completed March 27, 2026, 4:25 a.m.
Created at: March 22, 2026, 4:29 p.m.