Triple

T7871699
Position Surface form Disambiguated ID Type / Status
Subject Jacobi symbol E182750 entity
Predicate relatedConcept P37 FINISHED
Object Dirichlet character E459563 NE FINISHED

How this triple was built (2 steps)

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.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Dirichlet character | Statement: [Jacobi symbol, relatedConcept, Dirichlet character]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet character
Context triple: [Jacobi symbol, relatedConcept, Dirichlet character]
  • A. Dirichlet characters chosen
    Dirichlet characters are completely multiplicative periodic arithmetic functions modulo an integer, fundamental in analytic number theory for constructing Dirichlet L-functions and studying the distribution of primes in arithmetic progressions.
  • B. Dirichlet L-functions
    Dirichlet L-functions are complex analytic functions built from Dirichlet characters that generalize the Riemann zeta function and play a central role in number theory, particularly in the study of primes in arithmetic progressions.
  • C. Dirichlet
    Dirichlet was a 19th-century German mathematician renowned for foundational contributions to number theory and mathematical analysis, including Dirichlet's theorem on arithmetic progressions and the formalization of the concept of a function.
  • D. Dirichlet series
    A Dirichlet series is an infinite series of the form ∑ aₙ/nˢ, fundamental in analytic number theory for studying arithmetic functions and L-functions.
  • E. Legendre symbol
    The Legendre symbol is a number-theoretic function that indicates whether an integer is a quadratic residue modulo an odd prime, taking values 1, −1, or 0 accordingly.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

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.
NER Named-entity recognition batch_69cb39a5950481908399211c5dfe2569 completed March 31, 2026, 3:04 a.m.
NED1 Entity disambiguation (via context triple) batch_69cb5b6bc7248190adbf4377c52e16a9 completed March 31, 2026, 5:28 a.m.
Created at: March 30, 2026, 4:56 p.m.