Triple

T15918621
Position Surface form Disambiguated ID Type / Status
Subject Szekeres–Lindström theorem E386034 entity
Predicate relationTo P34778 FINISHED
Object Erdős–Ko–Rado theorem E554298 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: Erdős–Ko–Rado theorem | Statement: [Szekeres–Lindström theorem, relationTo, Erdős–Ko–Rado theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Erdős–Ko–Rado theorem
Context triple: [Szekeres–Lindström theorem, relationTo, Erdős–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–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.
  • D. 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.
  • 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 (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_69d86da686e4819097cbf3b1fc2d881d completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e1567ff9e48190b73cb101fc3f7b2b completed April 16, 2026, 9:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69ffb05d1fb481909b42bea774a15c70 completed May 9, 2026, 10:08 p.m.
Created at: April 10, 2026, 4:52 a.m.