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.