Triple

T14438380
Position Surface form Disambiguated ID Type / Status
Subject L-function E358024 entity
Predicate hasSpecialCase P7025 FINISHED
Object Artin L-function E899965 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: Artin L-function | Statement: [L-function, hasSpecialCase, Artin L-function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Artin L-function
Context triple: [L-function, hasSpecialCase, Artin L-function]
  • A. Artin L-functions chosen
    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.
  • 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. 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. Artin’s conjecture on L-functions
    Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
  • E. Hasse–Weil zeta function
    The Hasse–Weil zeta function is an analytic object in number theory that encodes arithmetic information about algebraic varieties over number fields, generalizing the Riemann zeta function and playing a central role in modern arithmetic geometry and conjectures like the Weil conjectures and the Birch–Swinnerton-Dyer conjecture.
  • 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_69d8279402a88190821ffa39ae15bccf completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de914a45ec81909ab8ccf302047d7f completed April 14, 2026, 7:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd5bd7f46881908df1a1cea7b6af9b completed May 8, 2026, 3:43 a.m.
Created at: April 10, 2026, 1:18 a.m.