Triple

T7030800
Position Surface form Disambiguated ID Type / Status
Subject Diophantine approximation E163264 entity
Predicate hasKeyResult P70725 FINISHED
Object Jarník–Besicovitch theorem
The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.
E637306 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: Jarník–Besicovitch theorem | Statement: [Diophantine approximation, hasKeyResult, Jarník–Besicovitch theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Jarník–Besicovitch theorem
Context triple: [Diophantine approximation, hasKeyResult, Jarník–Besicovitch theorem]
  • A. Minkowski’s theorem on convex sets
    Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
  • B. 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.
  • C. 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.
  • 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. Radon’s theorem
    Radon’s theorem is a fundamental result in convex geometry stating that any set of sufficiently many points in Euclidean space can be partitioned into two disjoint subsets whose convex hulls intersect.
  • 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: Jarník–Besicovitch theorem
Triple: [Diophantine approximation, hasKeyResult, Jarník–Besicovitch theorem]
Generated description
The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Jarník–Besicovitch theorem
Target entity description: The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.
  • A. Minkowski’s theorem on convex sets
    Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
  • B. 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.
  • C. 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.
  • 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. Radon’s theorem
    Radon’s theorem is a fundamental result in convex geometry stating that any set of sufficiently many points in Euclidean space can be partitioned into two disjoint subsets whose convex hulls intersect.
  • 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_69c6885d691c81908cf7d31083113886 completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6e20ee1208190811be10a84e7d8a4 completed March 27, 2026, 8:01 p.m.
NED1 Entity disambiguation (via context triple) batch_69c775980920819081d31b8d2843fb3d completed March 28, 2026, 6:30 a.m.
NEDg Description generation batch_69c77aa1c704819088a9561ac55f9037 completed March 28, 2026, 6:52 a.m.
NED2 Entity disambiguation (via description) batch_69c77b082f3c8190a649297ce0f816bb completed March 28, 2026, 6:54 a.m.
Created at: March 27, 2026, 2:35 p.m.