Triple

T7078814
Position Surface form Disambiguated ID Type / Status
Subject Louis Mordell E164890 entity
Predicate notableWork P4 FINISHED
Object 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.
E640412 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: Three Lectures on Fermat's Last Theorem | Statement: [Louis Mordell, notableWork, Three Lectures on Fermat's Last Theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Three Lectures on Fermat's Last Theorem
Context triple: [Louis Mordell, notableWork, Three Lectures on Fermat's Last Theorem]
  • A. Three Pearls of Number Theory
    Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
  • B. Number Theory: An Approach through History from Hammurapi to Legendre
    "Number Theory: An Approach through History from Hammurapi to Legendre" is a historical and expository book by André Weil that traces the development of number theory from ancient Mesopotamia to the early 19th century.
  • C. Fermat's Last Theorem
    Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
  • D. Serre’s conjecture on Galois representations
    Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
  • E. 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.
  • 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: Three Lectures on Fermat's Last Theorem
Triple: [Louis Mordell, notableWork, Three Lectures on Fermat's Last Theorem]
Generated description
"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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Three Lectures on Fermat's Last Theorem
Target entity description: "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.
  • A. Three Pearls of Number Theory
    Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
  • B. Number Theory: An Approach through History from Hammurapi to Legendre
    "Number Theory: An Approach through History from Hammurapi to Legendre" is a historical and expository book by André Weil that traces the development of number theory from ancient Mesopotamia to the early 19th century.
  • C. Fermat's Last Theorem
    Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
  • D. Serre’s conjecture on Galois representations
    Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
  • E. 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.
  • 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_69c6887cbc6c8190bdfac42d940f4d8a completed March 27, 2026, 1:39 p.m.
NER Named-entity recognition batch_69c6e4ef47d48190b31125d1b57f7bec completed March 27, 2026, 8:13 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7947294d4819094d7cfb34efde915 completed March 28, 2026, 8:42 a.m.
NEDg Description generation batch_69c7954ee22c8190a531e30e8e54f7d5 completed March 28, 2026, 8:46 a.m.
NED2 Entity disambiguation (via description) batch_69c795fce734819086e20a916aa67f54 completed March 28, 2026, 8:49 a.m.
Created at: March 27, 2026, 2:40 p.m.