Triple

T6293562
Position Surface form Disambiguated ID Type / Status
Subject Bernoulli numbers E141076 entity
Predicate usedIn P98 FINISHED
Object Euler–Maclaurin summation formula E54271 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: Euler–Maclaurin summation formula | Statement: [Bernoulli numbers, usedIn, Euler–Maclaurin summation formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Euler–Maclaurin summation formula
Context triple: [Bernoulli numbers, usedIn, Euler–Maclaurin summation formula]
  • A. Euler–Maclaurin summation formula chosen
    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.
  • B. Poisson summation formula
    The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
  • C. 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.
  • D. Abel summation
    Abel summation is a method in mathematical analysis for assigning values to certain divergent series by considering the limit of their power series as the variable approaches 1 from below.
  • E. Cesàro summation
    Cesàro summation is a method of assigning finite values to certain divergent series by averaging their partial sums.
  • 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_69c008cdf2ac8190bb640c94478fb4ed completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c06438654481908c9833c5f0d61773 completed March 22, 2026, 9:50 p.m.
NED1 Entity disambiguation (via context triple) batch_69c51988f1388190b36212b0d9756863 completed March 26, 2026, 11:33 a.m.
Created at: March 22, 2026, 4:27 p.m.