Triple

T10991100

Position	Surface form	Disambiguated ID	Type / Status
Subject	generalized Riemann hypothesis	`E259754`	entity
Predicate	usedIn	`P98`	FINISHED
Object	algorithmic number theory Algorithmic number theory is a branch of mathematics and computer science that designs and analyzes efficient algorithms for solving problems involving integers, prime numbers, and related number-theoretic structures.	`E898460`	NE FINISHED

How this triple was built (4 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: algorithmic number theory | Statement: [generalized Riemann hypothesis, usedIn, algorithmic number theory]

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

Target entity: algorithmic number theory
Context triple: [generalized Riemann hypothesis, usedIn, algorithmic number theory]

A. algebraic number theory
Algebraic number theory is a branch of mathematics that studies algebraic structures related to algebraic integers and number fields, focusing on properties of integers through tools from abstract algebra.
B. analytic number theory
Analytic number theory is a branch of mathematics that uses tools from mathematical analysis to study the distribution and properties of integers, especially prime numbers.
C. A Course in Number Theory and Cryptography
A Course in Number Theory and Cryptography is a widely used textbook that introduces fundamental concepts of number theory with a strong emphasis on their applications to modern cryptography.
D. Algebraic Aspects of Cryptography
Algebraic Aspects of Cryptography is a graduate-level textbook that develops modern public-key cryptography using tools from algebraic number theory, algebraic geometry, and finite fields.
E. Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NEDg Description generation gpt-5.1

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: algorithmic number theory
Triple: [generalized Riemann hypothesis, usedIn, algorithmic number theory]

Generated description

Algorithmic number theory is a branch of mathematics and computer science that designs and analyzes efficient algorithms for solving problems involving integers, prime numbers, and related number-theoretic structures.

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

Target entity: algorithmic number theory
Target entity description: Algorithmic number theory is a branch of mathematics and computer science that designs and analyzes efficient algorithms for solving problems involving integers, prime numbers, and related number-theoretic structures.

A. algebraic number theory
Algebraic number theory is a branch of mathematics that studies algebraic structures related to algebraic integers and number fields, focusing on properties of integers through tools from abstract algebra.
B. analytic number theory
Analytic number theory is a branch of mathematics that uses tools from mathematical analysis to study the distribution and properties of integers, especially prime numbers.
C. A Course in Number Theory and Cryptography
A Course in Number Theory and Cryptography is a widely used textbook that introduces fundamental concepts of number theory with a strong emphasis on their applications to modern cryptography.
D. Algebraic Aspects of Cryptography
Algebraic Aspects of Cryptography is a graduate-level textbook that develops modern public-key cryptography using tools from algebraic number theory, algebraic geometry, and finite fields.
E. Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
F. None of above. chosen

Provenance (5 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_69d6aa8a6a548190a750f944ccdc8064`	completed	April 8, 2026, 7:20 p.m.
NER	Named-entity recognition	`batch_69d787b8d7088190b7d6b63c3bac4ad1`	completed	April 9, 2026, 11:04 a.m.
NED1	Entity disambiguation (via context triple)	`batch_69e34504ebec8190a78e4795765b0c24`	completed	April 18, 2026, 8:47 a.m.
NEDg	Description generation	`batch_69e3556fd3548190a33f04604be947cf`	completed	April 18, 2026, 9:57 a.m.
NED2	Entity disambiguation (via description)	`batch_69e3593b0f8481909ed7a90f8bb9839d`	completed	April 18, 2026, 10:13 a.m.

Created at: April 8, 2026, 9:24 p.m.