Triple

T7030726
Position Surface form Disambiguated ID Type / Status
Subject Multiplicative Number Theory E163262 entity
Predicate usesConcept P531 FINISHED
Object Riemann zeta function E47609 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: Riemann zeta function | Statement: [Multiplicative Number Theory, usesConcept, Riemann zeta function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riemann zeta function
Context triple: [Multiplicative Number Theory, usesConcept, Riemann zeta function]
  • A. Riemann zeta function chosen
    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.
  • B. 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.
  • C. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • D. Dirichlet eta function
    The Dirichlet eta function is an alternating Dirichlet series closely related to the Riemann zeta function and used in analytic number theory, particularly for studying series convergence and analytic continuation.
  • E. Euler product formula for the Riemann zeta function
    The Euler product formula for the Riemann zeta function is a fundamental identity in analytic number theory that expresses the zeta function as an infinite product over all prime numbers, revealing a deep connection between primes and the distribution of integers.
  • 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_69c6e20ee1208190811be10a84e7d8a4 completed March 27, 2026, 8:01 p.m.
NED1 Entity disambiguation (via context triple) batch_69c775980920819081d31b8d2843fb3d completed March 28, 2026, 6:30 a.m.
Created at: March 27, 2026, 2:35 p.m.