Triple

T17671631

Position	Surface form	Disambiguated ID	Type / Status
Subject	Goro Shimura	`E440532`	entity
Predicate	notableWork	`P4`	FINISHED
Object	Arithmetic of Elliptic Curves "Arithmetic of Elliptic Curves" is a foundational monograph in number theory that systematically develops the theory of elliptic curves and their arithmetic properties.	`E1281169`	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: Arithmetic of Elliptic Curves | Statement: [Goro Shimura, notableWork, Arithmetic of Elliptic Curves]

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

Target entity: Arithmetic of Elliptic Curves
Context triple: [Goro Shimura, notableWork, Arithmetic of Elliptic Curves]

A. Introduction to Elliptic Curves and Modular Forms
Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
B. Lectures on Elliptic Curves
Lectures on Elliptic Curves is a classic introductory monograph by J. W. S. Cassels that systematically develops the arithmetic theory of elliptic curves for advanced undergraduates and beginning graduate students in number theory.
C. A Course in Arithmetic
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
D. Cassels–Fröhlich: Algebraic Number Theory
Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
E. 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.
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: Arithmetic of Elliptic Curves
Triple: [Goro Shimura, notableWork, Arithmetic of Elliptic Curves]

Generated description

"Arithmetic of Elliptic Curves" is a foundational monograph in number theory that systematically develops the theory of elliptic curves and their arithmetic properties.

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

Target entity: Arithmetic of Elliptic Curves
Target entity description: "Arithmetic of Elliptic Curves" is a foundational monograph in number theory that systematically develops the theory of elliptic curves and their arithmetic properties.

A. Introduction to Elliptic Curves and Modular Forms
Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
B. Lectures on Elliptic Curves
Lectures on Elliptic Curves is a classic introductory monograph by J. W. S. Cassels that systematically develops the arithmetic theory of elliptic curves for advanced undergraduates and beginning graduate students in number theory.
C. A Course in Arithmetic
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
D. Cassels–Fröhlich: Algebraic Number Theory
Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
E. 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.
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_69d8b9e87e18819087104a44dc4dc5b1`	completed	April 10, 2026, 8:50 a.m.
NER	Named-entity recognition	`batch_69e46f69b11c8190b09add33f81776b3`	completed	April 19, 2026, 6 a.m.
NED1	Entity disambiguation (via context triple)	`batch_6a02166234f0819099c452808234e3e4`	completed	May 11, 2026, 5:48 p.m.
NEDg	Description generation	`batch_6a0217ca2ec881908573b0423c3610f7`	completed	May 11, 2026, 5:54 p.m.
NED2	Entity disambiguation (via description)	`batch_6a0218636e048190a48bc7f066c7bee1`	completed	May 11, 2026, 5:56 p.m.

Created at: April 10, 2026, 9:59 a.m.