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.