Triple
T25432538
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Liouville function |
E637296
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | completely multiplicative 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: completely multiplicative function Context triple: [Liouville function, instanceOf, completely multiplicative 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.
operation on arithmetic functions
An operation on arithmetic functions is a rule that combines one or more arithmetic functions (defined on the positive integers) to produce a new arithmetic function, such as via addition, multiplication, convolution, or composition.
-
C.
multiplicative character modulo p
A multiplicative character modulo p is a homomorphism from the multiplicative group of nonzero residues modulo a prime p to the complex numbers of absolute value 1, extended by defining its value at 0 (often as 0).
-
D.
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.
-
E.
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.
- 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_69e75db58a1c8190891b9ff7c2f8414e |
completed | April 21, 2026, 11:21 a.m. |
Created at: April 21, 2026, 1:58 p.m.