Triple

T22423130
Position Surface form Disambiguated ID Type / Status
Subject Erdős–Kac theorem E554297 entity
Predicate hasGeneralizations P2372 FINISHED
Object Kubilius model in probabilistic number theory — NE NERFINISHED

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: Kubilius model in probabilistic number theory | Statement: [Erdős–Kac theorem, hasGeneralizations, Kubilius model in probabilistic number theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Kubilius model in probabilistic number theory
Context triple: [Erdős–Kac theorem, hasGeneralizations, Kubilius model in probabilistic number theory]
  • A. Turán–Kubilius inequality chosen
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • B. 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.
  • C. Statistical Independence in Probability, Analysis and Number Theory
    "Statistical Independence in Probability, Analysis and Number Theory" is a mathematical monograph by Mark Kac that explores the concept of independence across probability theory, real analysis, and number theory.
  • 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.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e11e4f2d0c819091aa3558ea2ee630 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f15a2af620819083338127e78137dc completed April 29, 2026, 1:08 a.m.
Created at: April 16, 2026, 8:47 p.m.