Triple

T2815494
Position Surface form Disambiguated ID Type / Status
Subject Euler–Maclaurin summation formula E54271 entity
Predicate relatedTo P37 FINISHED
Object Faulhaber's formula 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: Faulhaber's formula | Statement: [Euler–Maclaurin summation formula, relatedTo, Faulhaber's formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Faulhaber's formula
Context triple: [Euler–Maclaurin summation formula, relatedTo, Faulhaber's formula]
  • A. 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.
  • B. 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.
  • C. Vandermonde's identity
    Vandermonde's identity is a fundamental combinatorial formula that expresses a binomial coefficient with a sum index as a sum of products of binomial coefficients, often visualized via counting arguments or generating functions.
  • D. Pascal's triangle
    Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
  • E. Pochhammer symbol
    The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
  • 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_69ab49de0af08190b3da69683be1e728 completed March 6, 2026, 9:40 p.m.
NER Named-entity recognition batch_69abde4d29488190a32461906dd9ea7e completed March 7, 2026, 8:14 a.m.
NED1 Entity disambiguation (via context triple) batch_69afce9f964081909e422aaf1f026dbb completed March 10, 2026, 7:56 a.m.
Created at: March 6, 2026, 9:59 p.m.