Triple

T8733461
Position Surface form Disambiguated ID Type / Status
Subject Hasse–Weil zeta function E207313 entity
Predicate specialCase P7025 FINISHED
Object Dedekind zeta function for number fields E262117 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: Dedekind zeta function for number fields | Statement: [Hasse–Weil zeta function, specialCase, Dedekind zeta function for number fields]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dedekind zeta function for number fields
Context triple: [Hasse–Weil zeta function, specialCase, Dedekind zeta function for number fields]
  • A. Dedekind zeta functions chosen
    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.
  • B. 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.
  • 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. 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.
  • E. Furtwängler’s theorem in class field theory
    Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
  • 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_69ca8358e4008190898471a59b96c301 completed March 30, 2026, 2:06 p.m.
NER Named-entity recognition batch_69cc5d2a26988190acfda17f232e610a completed March 31, 2026, 11:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69cf292d71ec819082095cb7b8b2d39c completed April 3, 2026, 2:42 a.m.
Created at: March 30, 2026, 6:37 p.m.