Triple
T12596980
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jordan’s totient functions |
E300758
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | number-theoretic functions |
C24992
|
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: number-theoretic functions Context triple: [Jordan’s totient functions, instanceOf, number-theoretic functions]
-
A.
arithmetical function
chosen
An arithmetical function is a function defined on the positive integers that assigns to each integer a (usually complex or real) value, often encoding number-theoretic properties such as divisors, primes, or multiplicative structure.
-
B.
Dirichlet series
A Dirichlet series is an infinite series of the form ∑ₙ₌₁^∞ aₙ n^(-s), where s is a complex variable and aₙ are complex coefficients, used extensively in analytic number theory to study arithmetic functions and L-functions.
-
C.
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.
-
D.
number theory work
A number theory work is a scholarly text or study focused on the properties, relationships, and structures of integers and related mathematical objects.
-
E.
L-function
An L-function is a complex analytic function, typically expressed as a Dirichlet series with an Euler product, that encodes deep arithmetic information about objects such as numbers, fields, or algebraic varieties.
- 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_69d7bdea2ca881908f379526c13b1145 |
completed | April 9, 2026, 2:55 p.m. |
Created at: April 9, 2026, 5:08 p.m.