Triple

T3757272
Position Surface form Disambiguated ID Type / Status
Subject George Szekeres E82077 entity
Predicate notableWork P4 FINISHED
Object 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.
E386034 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: Szekeres–Lindström theorem | Statement: [George Szekeres, notableWork, Szekeres–Lindström theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Szekeres–Lindström theorem
Context triple: [George Szekeres, notableWork, Szekeres–Lindström theorem]
  • A. de Bruijn–van Aardenne–Ehrenfest theorem
    The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
  • B. 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.
  • C. Ky Fan’s lemma
    Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
  • D. Hamilton’s compactness theorem
    Hamilton’s compactness theorem is a fundamental result in geometric analysis that provides conditions under which a sequence of Riemannian manifolds with controlled curvature and injectivity radius admits a smoothly convergent subsequence.
  • E. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • 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: Szekeres–Lindström theorem
Triple: [George Szekeres, notableWork, Szekeres–Lindström theorem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Szekeres–Lindström theorem
Target entity description: 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.
  • A. de Bruijn–van Aardenne–Ehrenfest theorem
    The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
  • B. 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.
  • C. Ky Fan’s lemma
    Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
  • D. Hamilton’s compactness theorem
    Hamilton’s compactness theorem is a fundamental result in geometric analysis that provides conditions under which a sequence of Riemannian manifolds with controlled curvature and injectivity radius admits a smoothly convergent subsequence.
  • E. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • 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_69ad8b1db40081908b61ffa6b78afd4d completed March 8, 2026, 2:43 p.m.
NER Named-entity recognition batch_69adcbbe7a6081909b0f835a77941300 completed March 8, 2026, 7:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69b4e50bfdb0819097bdfdd38f553ada completed March 14, 2026, 4:33 a.m.
NEDg Description generation batch_69b4e6c7164881909f14bf5b57916ae3 completed March 14, 2026, 4:40 a.m.
NED2 Entity disambiguation (via description) batch_69b4e74df9b481909d5286c64ae6d91a completed March 14, 2026, 4:42 a.m.
Created at: March 8, 2026, 3:35 p.m.