Triple

T10388773

Position	Surface form	Disambiguated ID	Type / Status
Subject	Weil conjectures	`E244835`	entity
Predicate	hasPart	`P35`	FINISHED
Object	Riemann hypothesis over finite fields The Riemann hypothesis over finite fields is a statement about the location of zeros of zeta functions of varieties over finite fields, asserting they lie on specific “critical lines” analogous to the classical Riemann hypothesis and forming a key component of the Weil conjectures.	`E244835`	NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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: Riemann hypothesis over finite fields | Statement: [Weil conjectures, hasPart, Riemann hypothesis over finite fields]

Disambiguation candidates (2 decisions)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Riemann hypothesis over finite fields
Context triple: [Weil conjectures, hasPart, Riemann hypothesis over finite fields]

A. 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.
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. Siegel’s theorem on zeros of L-functions
Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
D. Hasse–Weil bound for abelian varieties
The Hasse–Weil bound for abelian varieties is a fundamental result in arithmetic geometry that gives sharp estimates for the number of rational points on abelian varieties over finite fields in terms of their dimension and the field size.
E. Sato–Tate distribution (for families of elliptic curves)
The Sato–Tate distribution (for families of elliptic curves) is a probabilistic law describing how the normalized Frobenius traces (or equivalently, the angles in the Hasse bound) of elliptic curves are distributed, typically following a specific sine-squared measure on the interval [0, π].
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Riemann hypothesis over finite fields
Target entity description: The Riemann hypothesis over finite fields is a statement about the location of zeros of zeta functions of varieties over finite fields, asserting they lie on specific “critical lines” analogous to the classical Riemann hypothesis and forming a key component of the Weil conjectures.

A. 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.
B. Weil conjectures chosen
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. Siegel’s theorem on zeros of L-functions
Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
D. Hasse–Weil bound for abelian varieties
The Hasse–Weil bound for abelian varieties is a fundamental result in arithmetic geometry that gives sharp estimates for the number of rational points on abelian varieties over finite fields in terms of their dimension and the field size.
E. Sato–Tate distribution (for families of elliptic curves)
The Sato–Tate distribution (for families of elliptic curves) is a probabilistic law describing how the normalized Frobenius traces (or equivalently, the angles in the Hasse bound) of elliptic curves are distributed, typically following a specific sine-squared measure on the interval [0, π].
F. None of above.

How the object was described

The object's one-sentence description was generated by prompting gpt-5.1 with the object name and this triple as context.

Instruction

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Input

Entity: Riemann hypothesis over finite fields
Triple: [Weil conjectures, hasPart, Riemann hypothesis over finite fields]

Generated description

The Riemann hypothesis over finite fields is a statement about the location of zeros of zeta functions of varieties over finite fields, asserting they lie on specific “critical lines” analogous to the classical Riemann hypothesis and forming a key component of the Weil conjectures.

Provenance (5 batches)

Stage	Batch ID	Job type	Status
creating	`batch_69d381b5116081908d85227bab6d3c0c`	elicitation	completed
NER	`batch_69d4e9a59d688190b1da1ea0ed48fafa`	ner	completed
NED1	`batch_69d795b2423c8190a7c0e9b6fcbcc6db`	ned_source_triple	completed
NED2	`batch_69d79aa0cc5481908bc14cda8fb6e8b1`	ned_description	completed
NEDg	`batch_69d7998acbf881909b6f063c4bf2d0a6`	nedg	completed

Created at: April 6, 2026, 12:05 p.m.