Triple

T21046821
Position Surface form Disambiguated ID Type / Status
Subject Sperner family E518470 entity
Predicate relatedConcept P37 FINISHED
Object Erdos–Ko–Rado theorem — NE NERFINISHED

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: Erdos–Ko–Rado theorem | Statement: [Sperner family, relatedConcept, Erdos–Ko–Rado theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Erdos–Ko–Rado theorem
Context triple: [Sperner family, relatedConcept, Erdos–Ko–Rado theorem]
  • A. Erdős–Ko–Rado theorem chosen
    The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
  • B. Turán's theorem
    Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
  • C. Erdős–Stone theorem
    The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
  • D. Erdős–Rado theorem
    The Erdős–Rado theorem is a fundamental result in combinatorial set theory that generalizes Ramsey’s theorem to infinite cardinals, establishing powerful partition relations for large sets.
  • E. Sperner family
    A Sperner family is a collection of subsets of a finite set in which no subset is contained within another, central in extremal set theory and combinatorics.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e0b50438e08190917e2538bb8bc034 completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e6fcf4d26481908b639996500a8319 completed April 21, 2026, 4:28 a.m.
Created at: April 16, 2026, 2:34 p.m.