Triple

T15741749
Position Surface form Disambiguated ID Type / Status
Subject Ramsey theory E381617 entity
Predicate hasCentralConcept P531 FINISHED
Object Ramsey multiplicity
Ramsey multiplicity is a concept in Ramsey theory that quantifies the minimum number of monochromatic substructures (such as cliques) that must appear in any edge-coloring of a large enough complete graph.
E1174203 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: Ramsey multiplicity | Statement: [Ramsey theory, hasCentralConcept, Ramsey multiplicity]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ramsey multiplicity
Context triple: [Ramsey theory, hasCentralConcept, Ramsey multiplicity]
  • A. Ramsey theory
    Ramsey theory is a branch of combinatorics that studies the conditions under which order or structure must appear within sufficiently large or complex mathematical objects.
  • B. Graham–Rothschild theorem
    The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
  • C. 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.
  • D. Szemerédi's theorem
    Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
  • E. 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.
  • 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: Ramsey multiplicity
Triple: [Ramsey theory, hasCentralConcept, Ramsey multiplicity]
Generated description
Ramsey multiplicity is a concept in Ramsey theory that quantifies the minimum number of monochromatic substructures (such as cliques) that must appear in any edge-coloring of a large enough complete graph.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Ramsey multiplicity
Target entity description: Ramsey multiplicity is a concept in Ramsey theory that quantifies the minimum number of monochromatic substructures (such as cliques) that must appear in any edge-coloring of a large enough complete graph.
  • A. Ramsey theory
    Ramsey theory is a branch of combinatorics that studies the conditions under which order or structure must appear within sufficiently large or complex mathematical objects.
  • B. Graham–Rothschild theorem
    The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
  • C. 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.
  • D. Szemerédi's theorem
    Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
  • E. 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.
  • 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_69ff846436e48190b711da134c9a3b81 completed May 9, 2026, 7 p.m.
Created at: April 10, 2026, 4:46 a.m.