Triple

T7030757
Position Surface form Disambiguated ID Type / Status
Subject Multiplicative Number Theory E163262 entity
Predicate hasTextbook P5478 FINISHED
Object Multiplicative Number Theory II. Analytic and Probabilistic Number Theory (Hugh L. Montgomery, Robert C. Vaughan) E638640 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: Multiplicative Number Theory II. Analytic and Probabilistic Number Theory (Hugh L. Montgomery, Robert C. Vaughan) | Statement: [Multiplicative Number Theory, hasTextbook, Multiplicative Number Theory II. Analytic and Probabilistic Number Theory (Hugh L. Montgomery, Robert C. Vaughan)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Multiplicative Number Theory II. Analytic and Probabilistic Number Theory (Hugh L. Montgomery, Robert C. Vaughan)
Context triple: [Multiplicative Number Theory, hasTextbook, Multiplicative Number Theory II. Analytic and Probabilistic Number Theory (Hugh L. Montgomery, Robert C. Vaughan)]
  • A. Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan) chosen
    Multiplicative Number Theory I. Classical Theory (by Hugh L. Montgomery and Robert C. Vaughan) is a foundational graduate-level textbook that systematically develops the classical theory of multiplicative number theory, including Dirichlet characters, L-functions, and the distribution of prime numbers.
  • B. Multiplicative Number Theory
    Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
  • C. Selberg–Delange method results
    Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
  • D. 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.
  • E. A. Ivić, The Riemann Zeta-Function
    "A. Ivić, The Riemann Zeta-Function" is a comprehensive monograph on the analytic theory of the Riemann zeta function, widely regarded as a standard modern reference in analytic number theory.
  • 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_69c6885d691c81908cf7d31083113886 completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6e77415e88190ab65137382f1b155 completed March 27, 2026, 8:24 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7943ca8548190877d2698265ce7da completed March 28, 2026, 8:41 a.m.
Created at: March 27, 2026, 2:35 p.m.