Triple

T16991858
Position Surface form Disambiguated ID Type / Status
Subject The Twelvefold Way E412211 entity
Predicate relatesTo P37 FINISHED
Object Stirling numbers of the second kind
Stirling numbers of the second kind are a family of combinatorial numbers that count the ways to partition a set of n labeled elements into k nonempty, unlabeled subsets.
E1245025 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: Stirling numbers of the second kind | Statement: [The Twelvefold Way, relatesTo, Stirling numbers of the second kind]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Stirling numbers of the second kind
Context triple: [The Twelvefold Way, relatesTo, Stirling numbers of the second kind]
  • A. Bell numbers
    Bell numbers are a sequence in combinatorics that count the number of ways to partition a finite set into nonempty, unlabeled subsets.
  • B. Catalan numbers
    Catalan numbers are a sequence of natural numbers that count a wide variety of combinatorial structures, such as correctly matched parentheses, binary tree shapes, and lattice path configurations.
  • C. 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.
  • D. Dedekind number
    A Dedekind number is the count of distinct monotone Boolean functions (or equivalently, antichains) on an n-element set, forming a rapidly growing sequence studied in combinatorics and lattice theory.
  • E. Pólya enumeration theorem
    The Pólya enumeration theorem is a fundamental result in combinatorics that counts distinct configurations of objects under group actions by using cycle index polynomials and generating 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: Stirling numbers of the second kind
Triple: [The Twelvefold Way, relatesTo, Stirling numbers of the second kind]
Generated description
Stirling numbers of the second kind are a family of combinatorial numbers that count the ways to partition a set of n labeled elements into k nonempty, unlabeled subsets.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Stirling numbers of the second kind
Target entity description: Stirling numbers of the second kind are a family of combinatorial numbers that count the ways to partition a set of n labeled elements into k nonempty, unlabeled subsets.
  • A. Bell numbers
    Bell numbers are a sequence in combinatorics that count the number of ways to partition a finite set into nonempty, unlabeled subsets.
  • B. Catalan numbers
    Catalan numbers are a sequence of natural numbers that count a wide variety of combinatorial structures, such as correctly matched parentheses, binary tree shapes, and lattice path configurations.
  • C. 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.
  • D. Dedekind number
    A Dedekind number is the count of distinct monotone Boolean functions (or equivalently, antichains) on an n-element set, forming a rapidly growing sequence studied in combinatorics and lattice theory.
  • E. Pólya enumeration theorem
    The Pólya enumeration theorem is a fundamental result in combinatorics that counts distinct configurations of objects under group actions by using cycle index polynomials and generating 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_69d886cb581c8190ab05f4b429c9cd85 completed April 10, 2026, 5:12 a.m.
NER Named-entity recognition batch_69e3d280e3348190a27bd5dc7cf87c0e completed April 18, 2026, 6:50 p.m.
NED1 Entity disambiguation (via context triple) batch_6a00dc14d5688190945f7ae72f724922 completed May 10, 2026, 7:27 p.m.
NEDg Description generation batch_6a0114d5aeb0819086f1a5d279ac0d0f completed May 10, 2026, 11:29 p.m.
NED2 Entity disambiguation (via description) batch_6a0115c967b0819088e2335fd45d755b completed May 10, 2026, 11:33 p.m.
Created at: April 10, 2026, 5:32 a.m.