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.