Triple

T10991122
Position Surface form Disambiguated ID Type / Status
Subject Dirichlet L-functions E259755 entity
Predicate basedOn P98 FINISHED
Object Dirichlet characters 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 characters | Statement: [Dirichlet L-functions, basedOn, Dirichlet characters]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet characters
Context triple: [Dirichlet L-functions, basedOn, Dirichlet characters]
  • 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. Hecke characters
    Hecke characters are generalized algebraic number field characters (or Grössencharaktere) that play a central role in class field theory and the study of L-functions.
  • 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. Dedekind zeta functions
    Dedekind zeta functions are number-theoretic functions attached to algebraic number fields that encode their arithmetic properties, such as the distribution of prime ideals and class numbers.
  • E. Chebyshev functions
    Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
  • 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d787b8d7088190b7d6b63c3bac4ad1 completed April 9, 2026, 11:04 a.m.
NED1 Entity disambiguation (via context triple) batch_69e3a9644ff08190a3005e4f6a8243fe completed April 18, 2026, 3:55 p.m.
Created at: April 8, 2026, 9:24 p.m.