Triple

T7304643
Position Surface form Disambiguated ID Type / Status
Subject J. W. S. Cassels E167942 entity
Predicate hasBibliographyItem P7332 FINISHED
Object Cassels, J. W. S., Lectures on Elliptic Curves
"Cassels, J. W. S., Lectures on Elliptic Curves" is a classic introductory monograph that systematically develops the arithmetic theory of elliptic curves, widely used as a foundational text in number theory.
E654587 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: Cassels, J. W. S., Lectures on Elliptic Curves | Statement: [J. W. S. Cassels, hasBibliographyItem, Cassels, J. W. S., Lectures on Elliptic Curves]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cassels, J. W. S., Lectures on Elliptic Curves
Context triple: [J. W. S. Cassels, hasBibliographyItem, Cassels, J. W. S., Lectures on Elliptic Curves]
  • A. 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.
  • 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. 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.
  • D. 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.
  • E. Neukirch: Algebraic Number Theory
    "Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
  • 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: Cassels, J. W. S., Lectures on Elliptic Curves
Triple: [J. W. S. Cassels, hasBibliographyItem, Cassels, J. W. S., Lectures on Elliptic Curves]
Generated description
"Cassels, J. W. S., Lectures on Elliptic Curves" is a classic introductory monograph that systematically develops the arithmetic theory of elliptic curves, widely used as a foundational text in number theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cassels, J. W. S., Lectures on Elliptic Curves
Target entity description: "Cassels, J. W. S., Lectures on Elliptic Curves" is a classic introductory monograph that systematically develops the arithmetic theory of elliptic curves, widely used as a foundational text in number theory.
  • A. 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.
  • 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. 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.
  • D. 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.
  • E. Neukirch: Algebraic Number Theory
    "Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
  • 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_69c6888c820881909fc68f689fe1c251 completed March 27, 2026, 1:39 p.m.
NER Named-entity recognition batch_69c6ebb352ec8190846eff044e08805e completed March 27, 2026, 8:42 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7e55bfccc8190a46067c60c3c1a3f completed March 28, 2026, 2:27 p.m.
NEDg Description generation batch_69c7e5fbe8a8819083a892f4e54013eb completed March 28, 2026, 2:30 p.m.
NED2 Entity disambiguation (via description) batch_69c7e69ca1ac8190a398da894c6cc04e completed March 28, 2026, 2:33 p.m.
Created at: March 27, 2026, 3:01 p.m.