Triple

T12138861
Position Surface form Disambiguated ID Type / Status
Subject Pafnuty Chebyshev E289130 entity
Predicate notableWork P4 FINISHED
Object Chebyshev’s theorem on the distribution of prime numbers E898473 NE FINISHED

How this triple was built (2 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: Chebyshev’s theorem on the distribution of prime numbers | Statement: [Pafnuty Chebyshev, notableWork, Chebyshev’s theorem on the distribution of prime numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Chebyshev’s theorem on the distribution of prime numbers
Context triple: [Pafnuty Chebyshev, notableWork, Chebyshev’s theorem on the distribution of prime numbers]
  • A. Chebyshev’s estimates for π(x) chosen
    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.
  • B. 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.
  • 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. 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.
  • E. Vinogradov's three-primes theorem
    Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d6ab4b5e4c81909950b17151eb0951 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9158eef48819083bdce283a363414 completed April 10, 2026, 3:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69f5f690ae408190966bb4fe8feaa7d2 completed May 2, 2026, 1:05 p.m.
Created at: April 8, 2026, 9:49 p.m.