Triple

T7861118
Position Surface form Disambiguated ID Type / Status
Subject Adrien-Marie Legendre E182500 entity
Predicate notableWork P4 FINISHED
Object Essai sur la théorie des nombres
Essai sur la théorie des nombres is a foundational 18th-century treatise on number theory by Adrien-Marie Legendre that systematically developed many key results in the field.
E695814 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: Essai sur la théorie des nombres | Statement: [Adrien-Marie Legendre, notableWork, Essai sur la théorie des nombres]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Essai sur la théorie des nombres
Context triple: [Adrien-Marie Legendre, notableWork, Essai sur la théorie des nombres]
  • A. “Le Grand Crible dans la Théorie Analytique des Nombres”
    “Le Grand Crible dans la Théorie Analytique des Nombres” is a foundational monograph in analytic number theory that develops and applies the large sieve method to problems about the distribution of prime numbers and related arithmetic sequences.
  • B. Disquisitiones Arithmeticae
    Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
  • C. An Introduction to the Theory of Numbers
    An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
  • D. Theorie der algebraischen Zahlen
    "Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
  • E. Über die Anzahl der Primzahlen unter einer gegebenen Grösse
    Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
  • 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: Essai sur la théorie des nombres
Triple: [Adrien-Marie Legendre, notableWork, Essai sur la théorie des nombres]
Generated description
Essai sur la théorie des nombres is a foundational 18th-century treatise on number theory by Adrien-Marie Legendre that systematically developed many key results in the field.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Essai sur la théorie des nombres
Target entity description: Essai sur la théorie des nombres is a foundational 18th-century treatise on number theory by Adrien-Marie Legendre that systematically developed many key results in the field.
  • A. “Le Grand Crible dans la Théorie Analytique des Nombres”
    “Le Grand Crible dans la Théorie Analytique des Nombres” is a foundational monograph in analytic number theory that develops and applies the large sieve method to problems about the distribution of prime numbers and related arithmetic sequences.
  • B. Disquisitiones Arithmeticae
    Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
  • C. An Introduction to the Theory of Numbers
    An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
  • D. Theorie der algebraischen Zahlen
    "Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
  • E. Über die Anzahl der Primzahlen unter einer gegebenen Grösse
    Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
  • 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_69ca82887fd48190975896bf38c4596b completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb36bcb5cc8190a8a384ce0f020b9f completed March 31, 2026, 2:51 a.m.
NED1 Entity disambiguation (via context triple) batch_69cb5b4138d081908a5ff16b79f0a0c8 completed March 31, 2026, 5:27 a.m.
NEDg Description generation batch_69cb5f1c9ef08190b1b79482f39966c7 completed March 31, 2026, 5:43 a.m.
NED2 Entity disambiguation (via description) batch_69cb767b198481909cfc1f7a44e6f0d8 completed March 31, 2026, 7:23 a.m.
Created at: March 30, 2026, 4:53 p.m.