Triple

T2394175
Position Surface form Disambiguated ID Type / Status
Subject Riemann zeta function E47609 entity
Predicate generalization P2372 FINISHED
Object Hasse–Weil L-functions E207313 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: Hasse–Weil L-functions | Statement: [Riemann zeta function, generalization, Hasse–Weil L-functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hasse–Weil L-functions
Context triple: [Riemann zeta function, generalization, Hasse–Weil L-functions]
  • A. Hasse–Weil zeta function chosen
    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.
  • B. Weil conjectures
    The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
  • C. Hasse bound for elliptic curves
    The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
  • D. Serre’s conjecture on Galois representations
    Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
  • E. Hasse–Arf theorem
    The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
  • 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_69a88a1c450c81909f61abb8b6863885 completed March 4, 2026, 7:38 p.m.
NER Named-entity recognition batch_69abc87827d88190bb2351a688e6de32 completed March 7, 2026, 6:40 a.m.
NED1 Entity disambiguation (via context triple) batch_69aeb3da0978819094584cb23194fb3a completed March 9, 2026, 11:49 a.m.
Created at: March 4, 2026, 7:57 p.m.