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.