Triple

T5896704
Position Surface form Disambiguated ID Type / Status
Subject Pál Erdős E131117 entity
Predicate knownFor P22 FINISHED
Object Erdős–Szekeres theorem 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 theorem | Statement: [Pál Erdős, knownFor, Erdős–Szekeres theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Erdős–Szekeres theorem
Context triple: [Pál Erdős, knownFor, Erdős–Szekeres theorem]
  • 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. 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.
  • D. Helly’s theorem
    Helly’s theorem is a fundamental result in convex geometry that gives conditions under which a family of convex sets in Euclidean space has a nonempty common intersection.
  • E. Sperner's lemma
    Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
  • 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_69c00857439c819095950754176aa58a completed March 22, 2026, 3:18 p.m.
NER Named-entity recognition batch_69c036f4b56c8190aa52c9460eae8fbe completed March 22, 2026, 6:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69c0b159cb908190b78b78d1e854212b completed March 23, 2026, 3:19 a.m.
Created at: March 22, 2026, 3:58 p.m.