Triple
T18479741
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Vinogradov's three-primes theorem |
E451525
|
entity |
| Predicate | appearsIn |
P795
|
FINISHED |
| Object |
Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers"
Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers" is a classic monograph in analytic number theory that develops powerful techniques of trigonometric (exponential) sums to tackle additive problems, including results on the representation of integers as sums of primes.
|
E1325996
|
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: Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers" | Statement: [Vinogradov's three-primes theorem, appearsIn, Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers"]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers" Context triple: [Vinogradov's three-primes theorem, appearsIn, Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers"]
-
A.
Vinogradov's three-primes theorem
Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
-
B.
Trigonometric Series, Vol. I
Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
-
C.
Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)
Multiplicative Number Theory I. Classical Theory (by Hugh L. Montgomery and Robert C. Vaughan) is a foundational graduate-level textbook that systematically develops the classical theory of multiplicative number theory, including Dirichlet characters, L-functions, and the distribution of prime numbers.
-
D.
van der Corput method for estimating exponential sums
The van der Corput method for estimating exponential sums is a classical analytic number theory technique that provides bounds for oscillatory sums by exploiting differencing and smoothness properties of the phase function.
-
E.
Trigonometric Series, Vol. II
"Trigonometric Series, Vol. II" is a classic advanced mathematics text by Antoni Zygmund that develops the modern theory of trigonometric series and Fourier analysis.
- 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: Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers" Triple: [Vinogradov's three-primes theorem, appearsIn, Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers"]
Generated description
Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers" is a classic monograph in analytic number theory that develops powerful techniques of trigonometric (exponential) sums to tackle additive problems, including results on the representation of integers as sums of primes.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers" Target entity description: Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers" is a classic monograph in analytic number theory that develops powerful techniques of trigonometric (exponential) sums to tackle additive problems, including results on the representation of integers as sums of primes.
-
A.
Vinogradov's three-primes theorem
Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
-
B.
Trigonometric Series, Vol. I
Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
-
C.
Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)
Multiplicative Number Theory I. Classical Theory (by Hugh L. Montgomery and Robert C. Vaughan) is a foundational graduate-level textbook that systematically develops the classical theory of multiplicative number theory, including Dirichlet characters, L-functions, and the distribution of prime numbers.
-
D.
van der Corput method for estimating exponential sums
The van der Corput method for estimating exponential sums is a classical analytic number theory technique that provides bounds for oscillatory sums by exploiting differencing and smoothness properties of the phase function.
-
E.
Trigonometric Series, Vol. II
"Trigonometric Series, Vol. II" is a classic advanced mathematics text by Antoni Zygmund that develops the modern theory of trigonometric series and Fourier analysis.
- 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_69d8d38465a0819099b9b42d2a662ac1 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e53066a7108190a50eda9b489c90ca |
completed | April 19, 2026, 7:43 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a043f2f64848190808075254008e6e1 |
completed | May 13, 2026, 9:06 a.m. |
| NEDg | Description generation | batch_6a043fb7db388190bb50cfade4f025f9 |
completed | May 13, 2026, 9:09 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a044063c6048190b65620af8ceed897 |
completed | May 13, 2026, 9:12 a.m. |
Created at: April 10, 2026, 11:35 a.m.