Triple

T14334498
Position Surface form Disambiguated ID Type / Status
Subject Ramanujan prime E355434 entity
Predicate relatedConcept P37 FINISHED
Object Chebyshev function E300761 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: Chebyshev function | Statement: [Ramanujan prime, relatedConcept, Chebyshev function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Chebyshev function
Context triple: [Ramanujan prime, relatedConcept, Chebyshev function]
  • A. Chebyshev functions chosen
    Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
  • B. 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.
  • C. von Mangoldt function Λ(n)
    The von Mangoldt function Λ(n) is an arithmetic function in number theory that encodes the distribution of prime powers by assigning log p to integers n that are powers of a prime p and 0 otherwise.
  • 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. Hurwitz zeta function
    The Hurwitz zeta function is a complex analytic function that generalizes the Riemann zeta function by introducing a shift parameter, playing a key role in analytic number theory and special function 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_69d8278fa2108190bc0d0e7939c1eb03 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de8c20d2148190bb534bef338e871d completed April 14, 2026, 6:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd469634688190980df59ee482b792 completed May 8, 2026, 2:12 a.m.
Created at: April 10, 2026, 1:13 a.m.