Triple

T15918500
Position Surface form Disambiguated ID Type / Status
Subject Happy Ending problem E386030 entity
Predicate relatedTo P37 FINISHED
Object Erdős–Szekeres numbers E386031 NE FINISHED

How this triple was built (2 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 numbers | Statement: [Happy Ending problem, relatedTo, Erdős–Szekeres numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Erdős–Szekeres numbers
Context triple: [Happy Ending problem, relatedTo, Erdős–Szekeres numbers]
  • 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. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • 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. Pósa’s theorem in graph theory
    Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
  • E. Erdős on Graphs: His Legacy
    Erdős on Graphs: His Legacy is a mathematical monograph by Fan Chung and Ronald Graham that surveys and extends Paul Erdős’s influential work in graph theory and combinatorics.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69ffc3bb7d608190babbea74a9ca9f4c completed May 9, 2026, 11:31 p.m.
Created at: April 10, 2026, 4:52 a.m.