Triple

T20523460
Position Surface form Disambiguated ID Type / Status
Subject Helge von Koch E503870 entity
Predicate hasWork P6260 FINISHED
Object On the distribution of prime numbers
"On the distribution of prime numbers" is a mathematical paper by Helge von Koch that investigates the behavior and density of prime numbers, notably relating them to the Riemann Hypothesis.
E1435908 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: On the distribution of prime numbers | Statement: [Helge von Koch, hasWork, On the distribution of prime numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: On the distribution of prime numbers
Context triple: [Helge von Koch, hasWork, On 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. 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.
  • C. 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.
  • D. 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.
  • E. Linnik’s theorem on the least prime in an arithmetic progression
    Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
  • 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: On the distribution of prime numbers
Triple: [Helge von Koch, hasWork, On the distribution of prime numbers]
Generated description
"On the distribution of prime numbers" is a mathematical paper by Helge von Koch that investigates the behavior and density of prime numbers, notably relating them to the Riemann Hypothesis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: On the distribution of prime numbers
Target entity description: "On the distribution of prime numbers" is a mathematical paper by Helge von Koch that investigates the behavior and density of prime numbers, notably relating them to the Riemann Hypothesis.
  • 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. 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.
  • C. 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.
  • D. 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.
  • E. Linnik’s theorem on the least prime in an arithmetic progression
    Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
  • 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_69e0b4b3a6e08190ae663701f50fab8e completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e69f471f18819091e8a57161fe0225 completed April 20, 2026, 9:48 p.m.
NED1 Entity disambiguation (via context triple) batch_6a089d43c6588190a4be58521ca67698 completed May 16, 2026, 4:37 p.m.
NEDg Description generation batch_6a089e00cde081908dca3893f03e3398 completed May 16, 2026, 4:40 p.m.
NED2 Entity disambiguation (via description) batch_6a089e8a05488190b3470f4ffb5927ce completed May 16, 2026, 4:42 p.m.
Created at: April 16, 2026, 11:36 a.m.