Triple
T2228029
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | André Weil |
E48698
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Basic Number Theory
Basic Number Theory is a foundational graduate-level text by André Weil that systematically develops algebraic number theory and related concepts with exceptional rigor and depth.
|
E244837
|
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: Basic Number Theory | Statement: [André Weil, notableWork, Basic Number Theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Basic Number Theory Context triple: [André Weil, notableWork, Basic Number Theory]
-
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.
Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
-
C.
Fermat's little theorem
Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
-
D.
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.
-
E.
Unsolved Problems in Number Theory
*Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
- 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: Basic Number Theory Triple: [André Weil, notableWork, Basic Number Theory]
Generated description
Basic Number Theory is a foundational graduate-level text by André Weil that systematically develops algebraic number theory and related concepts with exceptional rigor and depth.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Basic Number Theory Target entity description: Basic Number Theory is a foundational graduate-level text by André Weil that systematically develops algebraic number theory and related concepts with exceptional rigor and depth.
-
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.
Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
-
C.
Fermat's little theorem
Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
-
D.
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.
-
E.
Unsolved Problems in Number Theory
*Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
- 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_69a88aa51b388190949868ec9766e587 |
completed | March 4, 2026, 7:40 p.m. |
| NER | Named-entity recognition | batch_69abc0670ce48190b98814064bff0517 |
completed | March 7, 2026, 6:06 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ae6567b64c8190ab718f20bbf033df |
completed | March 9, 2026, 6:15 a.m. |
| NEDg | Description generation | batch_69ae666bd32c81909ff15201757a6c76 |
completed | March 9, 2026, 6:19 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ae66d8ba688190a2102c00fc6231c4 |
completed | March 9, 2026, 6:21 a.m. |
Created at: March 4, 2026, 7:47 p.m.