Triple

T22964933
Position Surface form Disambiguated ID Type / Status
Subject Bombieri–Vinogradov theorem E571012 entity
Predicate involves P1256 FINISHED
Object Dirichlet L-functions — NE NERFINISHED

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 L-functions | Statement: [Bombieri–Vinogradov theorem, involves, Dirichlet L-functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet L-functions
Context triple: [Bombieri–Vinogradov theorem, involves, Dirichlet L-functions]
  • A. Dirichlet L-functions chosen
    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.
  • B. L-functions
    L-functions are complex analytic functions, often arising from number theory and algebraic geometry, that encode deep arithmetic information and generalize the Riemann zeta function.
  • C. Artin L-functions
    Artin L-functions are complex analytic functions attached to Galois representations that generalize Dirichlet L-functions and play a central role in number theory and the study of arithmetic properties of fields.
  • D. Rankin–Selberg L-function
    The Rankin–Selberg L-function is an analytic number theory object constructed from pairs of automorphic forms (or representations), encoding deep arithmetic information through their convolution.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e245b212a88190b5259caf51606084 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f181f763688190aab8f444a1a71577 completed April 29, 2026, 3:58 a.m.
Created at: April 17, 2026, 3:47 p.m.