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.