Triple

T3884669
Position Surface form Disambiguated ID Type / Status
Subject Hugo Steinhaus E92909 entity
Predicate notableWork P4 FINISHED
Object Steinhaus chessboard theorem
The Steinhaus chessboard theorem is a combinatorial result in geometry and topology that gives conditions under which certain colored paths must exist on a checkerboard-like grid.
E394470 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: Steinhaus chessboard theorem | Statement: [Hugo Steinhaus, notableWork, Steinhaus chessboard theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Steinhaus chessboard theorem
Context triple: [Hugo Steinhaus, notableWork, Steinhaus chessboard theorem]
  • A. Conway circle theorem
    The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Conway's 99-graph problem
    Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
  • 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: Steinhaus chessboard theorem
Triple: [Hugo Steinhaus, notableWork, Steinhaus chessboard theorem]
Generated description
The Steinhaus chessboard theorem is a combinatorial result in geometry and topology that gives conditions under which certain colored paths must exist on a checkerboard-like grid.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Steinhaus chessboard theorem
Target entity description: The Steinhaus chessboard theorem is a combinatorial result in geometry and topology that gives conditions under which certain colored paths must exist on a checkerboard-like grid.
  • A. Conway circle theorem
    The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Conway's 99-graph problem
    Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
  • 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_69aed9697de0819087c2559295ff3d12 completed March 9, 2026, 2:30 p.m.
NER Named-entity recognition batch_69aeec92cc548190b88b899299e5ccdc completed March 9, 2026, 3:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69b5125bee048190ba7553797e9fd254 completed March 14, 2026, 7:46 a.m.
NEDg Description generation batch_69b512e3721c8190accd26499191c153 completed March 14, 2026, 7:48 a.m.
NED2 Entity disambiguation (via description) batch_69b513618b888190acda94dcc91d24d2 completed March 14, 2026, 7:50 a.m.
Created at: March 9, 2026, 3:20 p.m.