Triple

T15741747
Position Surface form Disambiguated ID Type / Status
Subject Ramsey theory E381617 entity
Predicate hasCentralConcept P531 FINISHED
Object 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.
E1173844 NE FINISHED

How this triple was built (4 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–Rado theorem | Statement: [Ramsey theory, hasCentralConcept, Erdős–Rado theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Erdős–Rado theorem
Context triple: [Ramsey theory, hasCentralConcept, Erdős–Rado theorem]
  • A. Graham–Rothschild theorem
    The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
  • B. Erdős–Ko–Rado theorem
    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.
  • 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. 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.
  • E. de Bruijn–Erdős theorem
    The de Bruijn–Erdős theorem is a fundamental result in combinatorics and graph theory that relates finite and infinite structures, notably asserting that certain properties of infinite graphs or set systems are determined by their finite substructures.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Erdős–Rado theorem
Triple: [Ramsey theory, hasCentralConcept, Erdős–Rado theorem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Erdős–Rado theorem
Target entity description: 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.
  • A. Graham–Rothschild theorem
    The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
  • B. Erdős–Ko–Rado theorem
    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.
  • 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. 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.
  • E. de Bruijn–Erdős theorem
    The de Bruijn–Erdős theorem is a fundamental result in combinatorics and graph theory that relates finite and infinite structures, notably asserting that certain properties of infinite graphs or set systems are determined by their finite substructures.
  • F. None of above. chosen

Provenance (5 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_69d86d9cdb648190bf3171be0bd7d872 completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e04fd97d6c8190b2fa6ca422bfe512 completed April 16, 2026, 2:56 a.m.
NED1 Entity disambiguation (via context triple) batch_69ff83056aa0819098b757ed125e61fe completed May 9, 2026, 6:55 p.m.
NEDg Description generation batch_69ff83ca33d08190816130bf2ea735df completed May 9, 2026, 6:58 p.m.
NED2 Entity disambiguation (via description) batch_69ff8469354c819080b8cfddb7c66be5 completed May 9, 2026, 7 p.m.
Created at: April 10, 2026, 4:46 a.m.