Triple

T3884668
Position Surface form Disambiguated ID Type / Status
Subject Hugo Steinhaus E92909 entity
Predicate notableWork P4 FINISHED
Object Steinhaus theorem
The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
E394469 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 theorem | Statement: [Hugo Steinhaus, notableWork, Steinhaus theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Steinhaus theorem
Context triple: [Hugo Steinhaus, notableWork, Steinhaus theorem]
  • A. Ulam problem in set theory
    The Ulam problem in set theory is a well-known question posed by Stanislaw Ulam concerning the structure and properties of measurable sets and functions, particularly in relation to homomorphisms and measure-theoretic regularity.
  • B. Alexandrov–Hausdorff theorem
    The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
  • C. 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.
  • D. 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.
  • E. Khinchin–Kolmogorov theorem
    The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
  • 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 theorem
Triple: [Hugo Steinhaus, notableWork, Steinhaus theorem]
Generated description
The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Steinhaus theorem
Target entity description: The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
  • A. Ulam problem in set theory
    The Ulam problem in set theory is a well-known question posed by Stanislaw Ulam concerning the structure and properties of measurable sets and functions, particularly in relation to homomorphisms and measure-theoretic regularity.
  • B. Alexandrov–Hausdorff theorem
    The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
  • C. 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.
  • D. 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.
  • E. Khinchin–Kolmogorov theorem
    The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
  • 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.