Triple

T2171617
Position Surface form Disambiguated ID Type / Status
Subject Riemann–Siegel formula E48437 entity
Predicate standardReference P33736 FINISHED
Object 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.
E244384 NE FINISHED

How this triple was built (4 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: A. Ivić, The Riemann Zeta-Function | Statement: [Riemann–Siegel formula, standardReference, A. Ivić, The Riemann Zeta-Function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: A. Ivić, The Riemann Zeta-Function
Context triple: [Riemann–Siegel formula, standardReference, A. Ivić, The Riemann Zeta-Function]
  • A. 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.
  • B. H. M. Edwards, Riemann’s Zeta Function
    *H. M. Edwards, Riemann’s Zeta Function* is a classic monograph that provides a rigorous, historically informed, and comprehensive study of the Riemann zeta function and the Riemann Hypothesis, widely regarded as a standard reference in analytic number theory.
  • C. 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.
  • D. Riemann zeta function
    The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
  • E. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: A. Ivić, The Riemann Zeta-Function
Triple: [Riemann–Siegel formula, standardReference, A. Ivić, The Riemann Zeta-Function]
Generated description
"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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: A. Ivić, The Riemann Zeta-Function
Target entity description: "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.
  • A. 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.
  • B. H. M. Edwards, Riemann’s Zeta Function
    *H. M. Edwards, Riemann’s Zeta Function* is a classic monograph that provides a rigorous, historically informed, and comprehensive study of the Riemann zeta function and the Riemann Hypothesis, widely regarded as a standard reference in analytic number theory.
  • C. 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.
  • D. Riemann zeta function
    The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
  • E. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • F. None of above. chosen

Provenance (5 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_69a88aa3faa48190995b233af6525815 completed March 4, 2026, 7:40 p.m.
NER Named-entity recognition batch_69abbec7f9088190b32127421e340788 completed March 7, 2026, 5:59 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae653b6ae48190ab5c7e6bf2dcfa6f completed March 9, 2026, 6:14 a.m.
NEDg Description generation batch_69ae66411d848190a529018ad3765597 completed March 9, 2026, 6:18 a.m.
NED2 Entity disambiguation (via description) batch_69ae66a751f881908fda164de72dac9b completed March 9, 2026, 6:20 a.m.
Created at: March 4, 2026, 7:45 p.m.