Triple

T7115739
Position Surface form Disambiguated ID Type / Status
Subject Thomas M. Cover E165813 entity
Predicate knownFor P22 FINISHED
Object Cover’s theorem on the separability of patterns
Cover’s theorem on the separability of patterns is a fundamental result in statistical learning theory stating that complex pattern-classification problems are more likely to be linearly separable when data are mapped into a higher-dimensional feature space.
E641827 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 on the separability of patterns | Statement: [Thomas M. Cover, knownFor, Cover’s theorem on the separability of patterns]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cover’s theorem on the separability of patterns
Context triple: [Thomas M. Cover, knownFor, Cover’s theorem on the separability of patterns]
  • A. Blum complexity measures
    Blum complexity measures are a formal framework in computational complexity theory that rigorously define and compare the resource usage (such as time or space) of algorithms via axiomatic conditions.
  • B. Probably Approximately Correct learning (PAC learning)
    Probably Approximately Correct (PAC) learning is a foundational framework in computational learning theory that formalizes what it means for an algorithm to efficiently learn a concept from examples with high probability and small error.
  • C. Wozencraft ensemble in coding theory
    The Wozencraft ensemble in coding theory is a family of randomly constructed linear codes introduced by John Wozencraft that plays a key role in analyzing the performance limits of coding schemes, particularly for achieving capacity on noisy channels.
  • D. P, NP, and NP-Completeness: The Basics of Complexity Theory
    "P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
  • E. Cascade-Correlation learning architecture
    Cascade-Correlation learning architecture is a neural network training method that incrementally builds its own topology by adding new hidden units during learning to improve performance.
  • 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 on the separability of patterns
Triple: [Thomas M. Cover, knownFor, Cover’s theorem on the separability of patterns]
Generated description
Cover’s theorem on the separability of patterns is a fundamental result in statistical learning theory stating that complex pattern-classification problems are more likely to be linearly separable when data are mapped into a higher-dimensional feature space.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cover’s theorem on the separability of patterns
Target entity description: Cover’s theorem on the separability of patterns is a fundamental result in statistical learning theory stating that complex pattern-classification problems are more likely to be linearly separable when data are mapped into a higher-dimensional feature space.
  • A. Blum complexity measures
    Blum complexity measures are a formal framework in computational complexity theory that rigorously define and compare the resource usage (such as time or space) of algorithms via axiomatic conditions.
  • B. Probably Approximately Correct learning (PAC learning)
    Probably Approximately Correct (PAC) learning is a foundational framework in computational learning theory that formalizes what it means for an algorithm to efficiently learn a concept from examples with high probability and small error.
  • C. Wozencraft ensemble in coding theory
    The Wozencraft ensemble in coding theory is a family of randomly constructed linear codes introduced by John Wozencraft that plays a key role in analyzing the performance limits of coding schemes, particularly for achieving capacity on noisy channels.
  • D. P, NP, and NP-Completeness: The Basics of Complexity Theory
    "P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
  • E. Cascade-Correlation learning architecture
    Cascade-Correlation learning architecture is a neural network training method that incrementally builds its own topology by adding new hidden units during learning to improve performance.
  • 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.