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.