Triple

T20439484
Position Surface form Disambiguated ID Type / Status
Subject Edmund Landau E501345 entity
Predicate notableWork P4 FINISHED
Object Handbuch der Lehre von der Verteilung der Primzahlen
Handbuch der Lehre von der Verteilung der Primzahlen is a classic early 20th-century monograph in analytic number theory that systematically develops the theory of the distribution of prime numbers.
E1430742 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: Handbuch der Lehre von der Verteilung der Primzahlen | Statement: [Edmund Landau, notableWork, Handbuch der Lehre von der Verteilung der Primzahlen]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Handbuch der Lehre von der Verteilung der Primzahlen
Context triple: [Edmund Landau, notableWork, Handbuch der Lehre von der Verteilung der Primzahlen]
  • A. 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.
  • B. 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.
  • C. “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.
  • D. Piatetski-Shapiro prime number theorem
    The Piatetski-Shapiro prime number theorem is a result in analytic number theory that establishes the existence of infinitely many primes among the values of certain non-integer power sequences, such as ⌊n^c⌋ for suitable real exponents c.
  • E. Chebyshev’s estimates for π(x)
    Chebyshev’s estimates for π(x) are 19th-century bounds on the prime-counting function that showed it grows on the order of x/log x and provided a crucial precursor to the prime number 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: Handbuch der Lehre von der Verteilung der Primzahlen
Triple: [Edmund Landau, notableWork, Handbuch der Lehre von der Verteilung der Primzahlen]
Generated description
Handbuch der Lehre von der Verteilung der Primzahlen is a classic early 20th-century monograph in analytic number theory that systematically develops the theory of the distribution of prime numbers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Handbuch der Lehre von der Verteilung der Primzahlen
Target entity description: Handbuch der Lehre von der Verteilung der Primzahlen is a classic early 20th-century monograph in analytic number theory that systematically develops the theory of the distribution of prime numbers.
  • A. 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.
  • B. 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.
  • C. “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.
  • D. Piatetski-Shapiro prime number theorem
    The Piatetski-Shapiro prime number theorem is a result in analytic number theory that establishes the existence of infinitely many primes among the values of certain non-integer power sequences, such as ⌊n^c⌋ for suitable real exponents c.
  • E. Chebyshev’s estimates for π(x)
    Chebyshev’s estimates for π(x) are 19th-century bounds on the prime-counting function that showed it grows on the order of x/log x and provided a crucial precursor to the prime number 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_69e0b4ab3cfc8190ac9bf32e932316b1 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e685f20fe08190b9370b523a20153d completed April 20, 2026, 8 p.m.
NED1 Entity disambiguation (via context triple) batch_6a0883fd1af88190a34aef615ec3a23e completed May 16, 2026, 2:49 p.m.
NEDg Description generation batch_6a0884d316148190b1fe155fc2dfbb7b completed May 16, 2026, 2:53 p.m.
NED2 Entity disambiguation (via description) batch_6a088565cbcc81909b4bbc286d272ef6 completed May 16, 2026, 2:55 p.m.
Created at: April 16, 2026, 11:31 a.m.