Triple
T7030866
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | George Pólya |
E163265
|
entity |
| Predicate | notableIdea |
P4
|
FINISHED |
| Object | Pólya enumeration theorem |
E586574
|
NE FINISHED |
How this triple was built (2 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: Pólya enumeration theorem | Statement: [George Pólya, notableIdea, Pólya enumeration theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Pólya enumeration theorem Context triple: [George Pólya, notableIdea, Pólya enumeration theorem]
-
A.
Pólya enumeration theorem
chosen
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.
-
B.
Burnside's lemma
Burnside's lemma is a result in group theory and combinatorics that counts distinct configurations under symmetries by averaging the number of fixed points of group actions.
-
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.
enumerative combinatorics
Enumerative combinatorics is a branch of mathematics focused on counting and characterizing discrete structures, often using generating functions, bijections, and algebraic techniques.
-
E.
Foundations of Combinatorial Theory
Foundations of Combinatorial Theory is a seminal mathematical work by Gian-Carlo Rota that helped establish modern combinatorics as a rigorous and unified field of study.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69c6885d691c81908cf7d31083113886 |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6e20ee1208190811be10a84e7d8a4 |
completed | March 27, 2026, 8:01 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c775980920819081d31b8d2843fb3d |
completed | March 28, 2026, 6:30 a.m. |
Created at: March 27, 2026, 2:35 p.m.