Triple
T33760792
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Arthur trace formula |
E865100
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | analytic tool in number theory |
C41099
|
CONCEPT FINISHED |
How this triple was built (1 step)
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.
CD
Concept disambiguation
gpt-5-mini-2025-08-07
Target class: analytic tool in number theory Context triple: [Arthur trace formula, instanceOf, analytic tool in number theory]
-
A.
object of analytic number theory
An object of analytic number theory is a mathematical entity—such as a function, sequence, or set of numbers—studied using tools of analysis (like complex analysis, Fourier analysis, or measure theory) to understand the distribution and properties of integers and related structures.
-
B.
analytic number theory technique
chosen
An analytic number theory technique is a method that applies tools from analysis—such as complex functions, series, and integrals—to study and solve problems about integers and their distribution.
-
C.
algorithm in number theory
An algorithm in number theory is a finite, well-defined computational procedure designed to solve problems involving integers and their properties, such as divisibility, primality, and modular relationships.
-
D.
phenomenon in analytic number theory
A phenomenon in analytic number theory is a recurring pattern or behavior in the distribution or properties of numbers—often primes or arithmetic functions—that is revealed and studied using tools from complex analysis and asymptotic methods.
-
E.
identity in analytic number theory
Identity in analytic number theory is a rigorously proven equality, often involving series, integrals, or arithmetic functions, that reveals structural relationships between number-theoretic objects and underpins analytic techniques such as transforms, convolutions, and explicit formulas.
- F. None of above.
Provenance (1 batch)
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_69f3498d3b748190aa3c4006c1f32f38 |
completed | April 30, 2026, 12:22 p.m. |
Created at: May 1, 2026, 1:45 a.m.