Triple

T8644704
Position Surface form Disambiguated ID Type / Status
Subject Deuring–Heilbronn phenomenon E204744 entity
Predicate involves P1256 FINISHED
Object Dirichlet L-function E259755 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 L-function | Statement: [Deuring–Heilbronn phenomenon, involves, Dirichlet L-function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet L-function
Context triple: [Deuring–Heilbronn phenomenon, involves, Dirichlet L-function]
  • 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. Liouville function
    The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
  • 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. Riemann zeta function
    The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
  • 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_69ca834ca1c88190a11ffb0200342fac completed March 30, 2026, 2:06 p.m.
NER Named-entity recognition batch_69cc479999c881908c0c4e01c07d02d4 completed March 31, 2026, 10:15 p.m.
NED1 Entity disambiguation (via context triple) batch_69cebc42922c819099a464d2e347dec4 completed April 2, 2026, 6:58 p.m.
Created at: March 30, 2026, 6:28 p.m.