Triple

T11440032
Position Surface form Disambiguated ID Type / Status
Subject C. A. Rogers E271118 entity
Predicate notableWork P4 FINISHED
Object Packing and Covering
"Packing and Covering" is a classic mathematical monograph by C. A. Rogers that systematically develops the theory of packing and covering problems in geometry and number theory.
E926681 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: Packing and Covering | Statement: [C. A. Rogers, notableWork, Packing and Covering]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Packing and Covering
Context triple: [C. A. Rogers, notableWork, Packing and Covering]
  • A. 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.
  • B. A Combinatorial Problem
    "A Combinatorial Problem" is a classic mathematical paper by N. G. de Bruijn that introduces and analyzes a fundamental counting problem in combinatorics.
  • C. 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.
  • D. 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.
  • E. Sperner family
    A Sperner family is a collection of subsets of a finite set in which no subset is contained within another, central in extremal set theory and combinatorics.
  • 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: Packing and Covering
Triple: [C. A. Rogers, notableWork, Packing and Covering]
Generated description
"Packing and Covering" is a classic mathematical monograph by C. A. Rogers that systematically develops the theory of packing and covering problems in geometry and number theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Packing and Covering
Target entity description: "Packing and Covering" is a classic mathematical monograph by C. A. Rogers that systematically develops the theory of packing and covering problems in geometry and number theory.
  • A. 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.
  • B. A Combinatorial Problem
    "A Combinatorial Problem" is a classic mathematical paper by N. G. de Bruijn that introduces and analyzes a fundamental counting problem in combinatorics.
  • C. 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.
  • D. 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.
  • E. Sperner family
    A Sperner family is a collection of subsets of a finite set in which no subset is contained within another, central in extremal set theory and combinatorics.
  • 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_69d6aadeef688190874bcecd88b3dd9b completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d80888190c8190b6365550ffe4931c completed April 9, 2026, 8:14 p.m.
NED1 Entity disambiguation (via context triple) batch_69e5d39554c48190969cc0ebd4dbc368 completed April 20, 2026, 7:19 a.m.
NEDg Description generation batch_69e5d91b047c81909ea4c7f114bfbba5 completed April 20, 2026, 7:43 a.m.
NED2 Entity disambiguation (via description) batch_69e5e2de4cd081908d30c44853565029 completed April 20, 2026, 8:25 a.m.
Created at: April 8, 2026, 9:35 p.m.