Triple

T23131722
Position Surface form Disambiguated ID Type / Status
Subject Hugh L. Montgomery E577185 entity
Predicate notableWork P4 FINISHED
Object Montgomery–Vaughan multiplicative number theory results 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 multiplicative number theory results | Statement: [Hugh L. Montgomery, notableWork, Montgomery–Vaughan multiplicative number theory results]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Montgomery–Vaughan multiplicative number theory results
Context triple: [Hugh L. Montgomery, notableWork, Montgomery–Vaughan multiplicative number theory results]
  • 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. 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.
  • E. Montgomery's pair correlation conjecture
    Montgomery's pair correlation conjecture is a deep number-theoretic prediction about the statistical spacing of the nontrivial zeros of the Riemann zeta function, linking them to eigenvalues of random matrices and suggesting profound connections between number theory and quantum physics.
  • 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.