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.