Triple
T12597119
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Chebyshev function θ(x) |
E300761
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | Chebyshev function |
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: Chebyshev function Context triple: [Chebyshev function θ(x), instanceOf, Chebyshev function]
-
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.
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.
-
C.
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.
-
D.
circle method
The circle method is an analytic number theory technique that uses integration over the unit circle in the complex plane to estimate the number of representations of integers by various arithmetic functions.
-
E.
special function
A special function is a mathematically well-studied function, often arising as a solution to differential equations or integrals, that has established names, properties, and applications across many areas of science and engineering.
- 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.