Triple
T14265430
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Wacław Sierpiński |
E353630
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Elementary Theory of Numbers
Elementary Theory of Numbers is a classic introductory textbook on number theory by Wacław Sierpiński, covering fundamental properties of integers and related topics in a rigorous yet accessible manner.
|
E1090233
|
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: Elementary Theory of Numbers | Statement: [Wacław Sierpiński, notableWork, Elementary Theory of Numbers]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Elementary Theory of Numbers Context triple: [Wacław Sierpiński, notableWork, Elementary Theory of Numbers]
-
A.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
-
B.
An Elementary Investigation of the Theory of Numbers
An Elementary Investigation of the Theory of Numbers is a foundational 19th-century treatise on number theory by mathematician Peter Barlow, covering properties of integers, prime numbers, and related arithmetic topics.
-
C.
Three Pearls of Number Theory
Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
-
D.
Essai sur la théorie des nombres
Essai sur la théorie des nombres is a foundational 18th-century treatise on number theory by Adrien-Marie Legendre that systematically developed many key results in the field.
-
E.
The Higher Arithmetic
The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
- 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: Elementary Theory of Numbers Triple: [Wacław Sierpiński, notableWork, Elementary Theory of Numbers]
Generated description
Elementary Theory of Numbers is a classic introductory textbook on number theory by Wacław Sierpiński, covering fundamental properties of integers and related topics in a rigorous yet accessible manner.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Elementary Theory of Numbers Target entity description: Elementary Theory of Numbers is a classic introductory textbook on number theory by Wacław Sierpiński, covering fundamental properties of integers and related topics in a rigorous yet accessible manner.
-
A.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
-
B.
An Elementary Investigation of the Theory of Numbers
An Elementary Investigation of the Theory of Numbers is a foundational 19th-century treatise on number theory by mathematician Peter Barlow, covering properties of integers, prime numbers, and related arithmetic topics.
-
C.
Three Pearls of Number Theory
Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
-
D.
Essai sur la théorie des nombres
Essai sur la théorie des nombres is a foundational 18th-century treatise on number theory by Adrien-Marie Legendre that systematically developed many key results in the field.
-
E.
The Higher Arithmetic
The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
- 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_69d8278c43e08190824146f4632b89a5 |
completed | April 9, 2026, 10:26 p.m. |
| NER | Named-entity recognition | batch_69de6357a8188190ba518a486521052b |
completed | April 14, 2026, 3:55 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd326551b08190ae8fe220a6422339 |
completed | May 8, 2026, 12:46 a.m. |
| NEDg | Description generation | batch_69fd3417e8e88190b099bfe4ba30f364 |
completed | May 8, 2026, 12:53 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69fd37df3dfc8190a594abb2c14e11bb |
completed | May 8, 2026, 1:09 a.m. |
Created at: April 10, 2026, 1:09 a.m.