Triple

T12138862
Position Surface form Disambiguated ID Type / Status
Subject Pafnuty Chebyshev E289130 entity
Predicate notableWork P4 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: [Pafnuty Chebyshev, notableWork, Chebyshev function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Chebyshev function
Context triple: [Pafnuty Chebyshev, notableWork, 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. 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.
  • D. 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.
  • E. Liouville function
    The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
  • 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_69d6ab4b5e4c81909950b17151eb0951 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9158eef48819083bdce283a363414 completed April 10, 2026, 3:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69f5f690ae408190966bb4fe8feaa7d2 completed May 2, 2026, 1:05 p.m.
Created at: April 8, 2026, 9:49 p.m.