Triple

T1233845
Position Surface form Disambiguated ID Type / Status
Subject Jakob Bernoulli E26502 entity
Predicate notableConcept P201 FINISHED
Object Bernoulli numbers E141076 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: Bernoulli numbers | Statement: [Jakob Bernoulli, notableConcept, Bernoulli numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bernoulli numbers
Context triple: [Jakob Bernoulli, notableConcept, Bernoulli numbers]
  • A. Bernoulli numbers chosen
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • B. 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.
  • C. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • D. 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.
  • E. Hardy–Ramanujan asymptotic formula
    The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
  • 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_69a4948571c88190a9191e451e6035fd completed March 1, 2026, 7:33 p.m.
NER Named-entity recognition batch_69a4be5d16ec819088056167c88d3318 completed March 1, 2026, 10:31 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac8f75778881908c9c3ea6f8b3392a completed March 7, 2026, 8:49 p.m.
Created at: March 1, 2026, 7:47 p.m.