Triple

T7030743
Position Surface form Disambiguated ID Type / Status
Subject Multiplicative Number Theory E163262 entity
Predicate methodUsed P859 FINISHED
Object Perron’s formula E451517 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: Perron’s formula | Statement: [Multiplicative Number Theory, methodUsed, Perron’s formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Perron’s formula
Context triple: [Multiplicative Number Theory, methodUsed, Perron’s formula]
  • A. Euler’s reflection formula
    Euler’s reflection formula is a fundamental identity in complex analysis that relates the values of the Gamma function at z and 1−z through the sine function, revealing a deep symmetry of the Gamma function.
  • B. Khinchin–Pollaczek formula
    The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
  • C. Tauberian theorems chosen
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • D. Euler–Maclaurin summation formula
    The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
  • 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.
  • 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.