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.