Triple
T7030755
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Multiplicative Number Theory |
E163262
|
entity |
| Predicate | hasTextbook |
P5478
|
FINISHED |
| Object | Multiplicative Number Theory (Harold Davenport) |
E163262
|
NE FINISHED |
How this triple was built (3 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: Multiplicative Number Theory (Harold Davenport) | Statement: [Multiplicative Number Theory, hasTextbook, Multiplicative Number Theory (Harold Davenport)]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Multiplicative Number Theory (Harold Davenport) Context triple: [Multiplicative Number Theory, hasTextbook, Multiplicative Number Theory (Harold Davenport)]
-
A.
Multiplicative Number Theory
chosen
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.
-
B.
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.
-
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.
Hardy–Littlewood circle method
The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
-
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.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasTextbook Context triple: [Multiplicative Number Theory, hasTextbook, Multiplicative Number Theory (Harold Davenport)]
-
A.
hasBook
Indicates that an entity possesses, owns, or is associated with a particular book.
-
B.
containsBook
chosen
Indicates that one entity (typically a container or collection) includes a specific book as part of its contents.
-
C.
notableTextbook
Indicates that a textbook is recognized as significant, influential, or widely used within its field or subject area.
-
D.
hasEducationalMaterial
Indicates that an entity provides, contains, or is associated with educational content or learning resources for another entity.
-
E.
hasThreeBooksWith
Indicates that two entities are related by one having exactly three books together with the other (e.g., jointly owned, shared, or associated as a group of three books).
- F. None of above.
Provenance (4 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_69c6885d691c81908cf7d31083113886 |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6e458ad9c81908c3f492b317ce291 |
completed | March 27, 2026, 8:11 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c775980920819081d31b8d2843fb3d |
completed | March 28, 2026, 6:30 a.m. |
| PD | Predicate disambiguation | batch_69c6e1b9a2488190aea351d96afa5a12 |
completed | March 27, 2026, 7:59 p.m. |
Created at: March 27, 2026, 2:35 p.m.