Triple

T9931947
Position Surface form Disambiguated ID Type / Status
Subject Koblitz curves E192666 entity
Predicate relatedTo P37 FINISHED
Object Frobenius endomorphism E790516 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: Frobenius endomorphism | Statement: [Koblitz curves, relatedTo, Frobenius endomorphism]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Frobenius endomorphism
Context triple: [Koblitz curves, relatedTo, Frobenius endomorphism]
  • A. Frobenius element chosen
    The Frobenius element is a distinguished element in a Galois group associated to an unramified prime, encoding how that prime splits in a field extension and playing a central role in algebraic number theory and arithmetic geometry.
  • 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. Hensel’s lemma
    Hensel’s lemma is a fundamental result in number theory and p-adic analysis that allows one to lift solutions of polynomial congruences modulo a prime power to higher powers, analogous to Newton’s method in the p-adic setting.
  • D. Levine-Fricke Field
    Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
  • E. Artin–Schreier theory
    Artin–Schreier theory is a branch of algebraic number theory and field theory that characterizes cyclic extensions of prime degree in fields of characteristic p using additive polynomials.
  • 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_69ca82dd978c8190947124ab0d3315ac completed March 30, 2026, 2:04 p.m.
NER Named-entity recognition batch_69cdb5b54f348190b8e70e7beff6098a completed April 2, 2026, 12:17 a.m.
NED1 Entity disambiguation (via context triple) batch_69d228d1620c8190ac7125b268dd6832 completed April 5, 2026, 9:18 a.m.
Created at: March 30, 2026, 8:43 p.m.