Triple
T7115740
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Thomas M. Cover |
E165813
|
entity |
| Predicate | theoremNamedAfter |
P29208
|
FINISHED |
| Object |
Cover’s theorem
Cover’s theorem is a result in statistical pattern recognition stating that data cast nonlinearly into a higher-dimensional space is more likely to be linearly separable than in a lower-dimensional space.
|
E641828
|
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: Cover’s theorem | Statement: [Thomas M. Cover, theoremNamedAfter, Cover’s theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cover’s theorem Context triple: [Thomas M. Cover, theoremNamedAfter, Cover’s theorem]
-
A.
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.
-
B.
Erdős–Ko–Rado theorem
The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
-
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.
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.
-
E.
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.
- 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: Cover’s theorem Triple: [Thomas M. Cover, theoremNamedAfter, Cover’s theorem]
Generated description
Cover’s theorem is a result in statistical pattern recognition stating that data cast nonlinearly into a higher-dimensional space is more likely to be linearly separable than in a lower-dimensional space.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Cover’s theorem Target entity description: Cover’s theorem is a result in statistical pattern recognition stating that data cast nonlinearly into a higher-dimensional space is more likely to be linearly separable than in a lower-dimensional space.
-
A.
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.
-
B.
Erdős–Ko–Rado theorem
The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
-
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.
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.
-
E.
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.
- 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_69c6888227bc8190a1394679e3116f90 |
completed | March 27, 2026, 1:39 p.m. |
| NER | Named-entity recognition | batch_69c6e5f401b881909ef4c2ab1e0750db |
completed | March 27, 2026, 8:17 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c79cbfc7a08190ab07f3d65aa79f16 |
completed | March 28, 2026, 9:17 a.m. |
| NEDg | Description generation | batch_69c79d0215888190b0e59c2584358a05 |
completed | March 28, 2026, 9:18 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c79d63b6dc8190b3b52ef6566ba490 |
completed | March 28, 2026, 9:20 a.m. |
Created at: March 27, 2026, 2:43 p.m.