Triple
T7871664
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jacobi symbol |
E182750
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | generalization of Legendre symbol |
C22185
|
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: generalization of Legendre symbol Context triple: [Jacobi symbol, instanceOf, generalization of Legendre symbol]
-
A.
quadratic character
chosen
A quadratic character is a group homomorphism from a multiplicative group (often of a field or modulo n) to {±1} that indicates whether elements are quadratic residues or non-residues.
-
B.
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).
-
C.
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.
-
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.
algebraic number field
An algebraic number field is a finite field extension of the rational numbers, obtained by adjoining to ℚ a root of a nonzero polynomial with rational (or integer) coefficients.
- 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_69ca82894d9081908a832bfce71a4714 |
completed | March 30, 2026, 2:02 p.m. |
Created at: March 30, 2026, 4:56 p.m.