Triple

T23131723
Position Surface form Disambiguated ID Type / Status
Subject Hugh L. Montgomery E577185 entity
Predicate notableWork P4 FINISHED
Object Montgomery–Vaughan book "Multiplicative Number Theory I. Classical Theory" 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: Montgomery–Vaughan book "Multiplicative Number Theory I. Classical Theory" | Statement: [Hugh L. Montgomery, notableWork, Montgomery–Vaughan book "Multiplicative Number Theory I. Classical Theory"]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Montgomery–Vaughan book "Multiplicative Number Theory I. Classical Theory"
Context triple: [Hugh L. Montgomery, notableWork, Montgomery–Vaughan book "Multiplicative Number Theory I. Classical Theory"]
  • 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. Iwaniec and Kowalski, Analytic Number Theory
    "Iwaniec and Kowalski, Analytic Number Theory" is a comprehensive graduate-level textbook that systematically develops modern analytic methods in number theory, including prime distribution, sieve methods, and L-functions.
  • 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. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function
    "E. C. Titchmarsh, The Theory of the Riemann Zeta-Function" is a classic monograph in analytic number theory that provides a comprehensive and authoritative treatment of the Riemann zeta function and related topics.
  • 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_69e245f7b0e481909c473ff4e6a54e2c completed April 17, 2026, 2:38 p.m.
NER Named-entity recognition batch_69f18e88909881908c695cd7d39d380c completed April 29, 2026, 4:52 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0c23f7dccc8190aaba967e73cc6892 completed May 19, 2026, 8:48 a.m.
Created at: April 17, 2026, 4 p.m.