Triple

T6327888
Position Surface form Disambiguated ID Type / Status
Subject stars and bars method E141902 entity
Predicate hasAlternativeName P39 FINISHED
Object balls and urns method E141902 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: balls and urns method | Statement: [stars and bars method, hasAlternativeName, balls and urns method]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: balls and urns method
Context triple: [stars and bars method, hasAlternativeName, balls and urns method]
  • A. stars and bars method chosen
    The stars and bars method is a classic combinatorial technique used to count the number of ways to distribute indistinguishable objects into distinct bins, often applied to problems involving nonnegative integer solutions to equations.
  • B. 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.
  • C. enumerative combinatorics
    Enumerative combinatorics is a branch of mathematics focused on counting and characterizing discrete structures, often using generating functions, bijections, and algebraic techniques.
  • D. multinomial theorem
    The multinomial theorem is a fundamental algebraic formula that generalizes the binomial theorem to express powers of sums with any number of terms using multinomial coefficients.
  • E. binomial theorem
    The binomial theorem is a fundamental algebraic formula that provides a systematic way to expand powers of binomial expressions, playing a key role in combinatorics and mathematical analysis.
  • 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_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.
Created at: March 22, 2026, 4:29 p.m.