Triple

T1281482
Position Surface form Disambiguated ID Type / Status
Subject Pierre de Fermat E27335 entity
Predicate notableWork P4 FINISHED
Object Fermat's little theorem
Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
E146189 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: Fermat's little theorem | Statement: [Pierre de Fermat, notableWork, Fermat's little theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fermat's little theorem
Context triple: [Pierre de Fermat, notableWork, Fermat's little theorem]
  • A. Gauss’s lemma in number theory
    Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
  • B. Euler’s totient function φ(n)
    Euler’s totient function φ(n) is a fundamental arithmetic function in number theory that counts the positive integers up to n that are relatively prime to n and plays a key role in topics such as modular arithmetic and cryptography.
  • C. Pierre de Fermat
    Pierre de Fermat was a 17th-century French mathematician renowned for his work in number theory, probability, and analytic geometry, and especially for Fermat's Last Theorem.
  • D. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • E. Kronecker–Weber theorem
    The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
  • 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: Fermat's little theorem
Triple: [Pierre de Fermat, notableWork, Fermat's little theorem]
Generated description
Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fermat's little theorem
Target entity description: Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
  • A. Gauss’s lemma in number theory
    Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
  • B. Euler’s totient function φ(n)
    Euler’s totient function φ(n) is a fundamental arithmetic function in number theory that counts the positive integers up to n that are relatively prime to n and plays a key role in topics such as modular arithmetic and cryptography.
  • C. Pierre de Fermat
    Pierre de Fermat was a 17th-century French mathematician renowned for his work in number theory, probability, and analytic geometry, and especially for Fermat's Last Theorem.
  • D. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • E. Kronecker–Weber theorem
    The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
  • 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_69a496d3710c8190955dee8bc0dacb50 completed March 1, 2026, 7:43 p.m.
NER Named-entity recognition batch_69a4c0b317788190a1672b5ee422a049 completed March 1, 2026, 10:41 p.m.
NED1 Entity disambiguation (via context triple) batch_69aca2fb746881909ac7a8dd672fc939 completed March 7, 2026, 10:13 p.m.
NEDg Description generation batch_69aca3752a3c81908bd6d9744ad5f5a2 completed March 7, 2026, 10:15 p.m.
NED2 Entity disambiguation (via description) batch_69aca3e44bf481908c5726adddc4b428 completed March 7, 2026, 10:17 p.m.
Created at: March 1, 2026, 7:50 p.m.