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.