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.