Triple
T15918539
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Erdős–Szekeres theorem |
E386031
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Erdős–Szekeres conjecture
The Erdős–Szekeres conjecture is an unsolved problem in combinatorial geometry that predicts the exact minimum number of points in general position in the plane needed to guarantee a convex polygon with a given number of vertices.
|
E386031
|
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–Szekeres conjecture | Statement: [Erdős–Szekeres theorem, relatedTo, Erdős–Szekeres conjecture]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Erdős–Szekeres conjecture Context triple: [Erdős–Szekeres theorem, relatedTo, Erdős–Szekeres conjecture]
-
A.
Erdős–Szekeres theorem
The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
-
B.
Conway's thrackle conjecture
Conway's thrackle conjecture is an unsolved problem in combinatorial geometry asserting that in any drawing of a graph where every pair of edges meets exactly once, the number of edges cannot exceed the number of vertices.
-
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.
Erdős–Turán conjecture
The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
-
E.
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.
- 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–Szekeres conjecture Triple: [Erdős–Szekeres theorem, relatedTo, Erdős–Szekeres conjecture]
Generated description
The Erdős–Szekeres conjecture is an unsolved problem in combinatorial geometry that predicts the exact minimum number of points in general position in the plane needed to guarantee a convex polygon with a given number of vertices.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Erdős–Szekeres conjecture Target entity description: The Erdős–Szekeres conjecture is an unsolved problem in combinatorial geometry that predicts the exact minimum number of points in general position in the plane needed to guarantee a convex polygon with a given number of vertices.
-
A.
Erdős–Szekeres theorem
chosen
The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
-
B.
Conway's thrackle conjecture
Conway's thrackle conjecture is an unsolved problem in combinatorial geometry asserting that in any drawing of a graph where every pair of edges meets exactly once, the number of edges cannot exceed the number of vertices.
-
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.
Erdős–Turán conjecture
The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
-
E.
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.
- F. None of above.
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_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_69ffe46b06688190a02fee3700efd709 |
completed | May 10, 2026, 1:50 a.m. |
| NEDg | Description generation | batch_69ffe87a898881909848233ef3d508d2 |
completed | May 10, 2026, 2:07 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ffe8b3cdec8190b29de77b4fd3ae87 |
completed | May 10, 2026, 2:08 a.m. |
Created at: April 10, 2026, 4:52 a.m.