Triple

T601760
Position Surface form Disambiguated ID Type / Status
Subject Jean-Baptiste Joseph Fourier E11507 entity
Predicate notableConcept P201 FINISHED
Object Fourier series expansion of periodic functions E173 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: Fourier series expansion of periodic functions | Statement: [Jean-Baptiste Joseph Fourier, notableConcept, Fourier series expansion of periodic functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fourier series expansion of periodic functions
Context triple: [Jean-Baptiste Joseph Fourier, notableConcept, Fourier series expansion of periodic functions]
  • A. Fourier analysis chosen
    Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
  • B. Fourier
    Fourier is a French surname most famously associated with Jean-Baptiste Joseph Fourier, the mathematician and physicist known for developing Fourier analysis and Fourier series.
  • C. Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
    Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
  • D. Euler’s formula for complex exponentials
    Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
  • E. 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.
  • 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_69a4932779b881908688590d59c71900 completed March 1, 2026, 7:27 p.m.
NER Named-entity recognition batch_69a49d7c08648190bbffc8adb4148987 completed March 1, 2026, 8:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69a52ea8dd8481909108a8873c5d49d5 completed March 2, 2026, 6:31 a.m.
Created at: March 1, 2026, 7:35 p.m.