Triple
T9931756
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Neal Koblitz |
E192662
|
entity |
| Predicate | authorOf |
P4244
|
FINISHED |
| Object |
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.
|
E831065
|
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: Introduction to Elliptic Curves and Modular Forms | Statement: [Neal Koblitz, authorOf, Introduction to Elliptic Curves and Modular Forms]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Introduction to Elliptic Curves and Modular Forms Context triple: [Neal Koblitz, authorOf, Introduction to Elliptic Curves and Modular Forms]
-
A.
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.
-
B.
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.
-
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.
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.
Three Lectures on Fermat's Last Theorem
"Three Lectures on Fermat's Last Theorem" is a classic expository work in number theory in which Louis Mordell surveys the history, methods, and partial results surrounding Fermat's Last Theorem prior to its eventual proof.
- 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: Introduction to Elliptic Curves and Modular Forms Triple: [Neal Koblitz, authorOf, Introduction to Elliptic Curves and Modular Forms]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Introduction to Elliptic Curves and Modular Forms Target entity description: 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.
-
A.
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.
-
B.
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.
-
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.
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.
Three Lectures on Fermat's Last Theorem
"Three Lectures on Fermat's Last Theorem" is a classic expository work in number theory in which Louis Mordell surveys the history, methods, and partial results surrounding Fermat's Last Theorem prior to its eventual proof.
- 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_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. |
| NEDg | Description generation | batch_69d22c3a6fc0819083a376736325a04e |
completed | April 5, 2026, 9:32 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69d22cabf39881908f45667751384df5 |
completed | April 5, 2026, 9:34 a.m. |
Created at: March 30, 2026, 8:43 p.m.