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.