Triple

T7420178
Position Surface form Disambiguated ID Type / Status
Subject Legendre symbol E171225 entity
Predicate relatedConcept P37 FINISHED
Object Dirichlet character modulo p 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 modulo p | Statement: [Legendre symbol, relatedConcept, Dirichlet character modulo p]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet character modulo p
Context triple: [Legendre symbol, relatedConcept, Dirichlet character modulo p]
  • 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. Gaussian periods
    Gaussian periods are special algebraic sums of roots of unity that play a key role in number theory, particularly in constructing regular polygons like the 17-gon with straightedge and compass and in understanding cyclotomic fields.
  • C. 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.
  • D. Dirichlet's theorem on arithmetic progressions
    Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
  • E. Chebotarev density theorem
    The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
  • 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_69c68a625d048190af70eb8b63bec5a0 completed March 27, 2026, 1:47 p.m.
NER Named-entity recognition batch_69c6f2ea61248190886e8e55b42ba5f1 completed March 27, 2026, 9:13 p.m.
NED1 Entity disambiguation (via context triple) batch_69c81ef7fc808190a564ab4d9d97ab37 completed March 28, 2026, 6:33 p.m.
Created at: March 27, 2026, 3:11 p.m.