Triple
T1403594
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Richard K. Guy |
E31640
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
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.
|
E160614
|
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: Unsolved Problems in Number Theory | Statement: [Richard K. Guy, notableWork, Unsolved Problems in Number Theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Unsolved Problems in Number Theory Context triple: [Richard K. Guy, notableWork, Unsolved Problems in 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.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
C.
Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
-
D.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
-
E.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
- 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: Unsolved Problems in Number Theory Triple: [Richard K. Guy, notableWork, Unsolved Problems in Number Theory]
Generated description
*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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Unsolved Problems in Number Theory Target entity description: *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.
-
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.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
C.
Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
-
D.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
-
E.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
- 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_69a49918e1f88190ba610f9dc8114578 |
completed | March 1, 2026, 7:52 p.m. |
| NER | Named-entity recognition | batch_69a4c3a0330c8190b22452d29c79fcf4 |
completed | March 1, 2026, 10:54 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69acde39d14c81909a76704c8e16c744 |
completed | March 8, 2026, 2:26 a.m. |
| NEDg | Description generation | batch_69acdfc287648190b9a7313a074ceea5 |
completed | March 8, 2026, 2:32 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ace0b0c14481909559f926c190c146 |
completed | March 8, 2026, 2:36 a.m. |
Created at: March 1, 2026, 7:59 p.m.