Triple

T5019711
Position Surface form Disambiguated ID Type / Status
Subject Harald Bohr E112818 entity
Predicate hasWork P6260 FINISHED
Object Almost Periodic Functions
Almost Periodic Functions is a foundational mathematical work by Harald Bohr that develops the theory of functions whose values recur with arbitrary precision over time, generalizing the concept of periodicity.
E486749 NE FINISHED

How this triple was built (4 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: Almost Periodic Functions | Statement: [Harald Bohr, hasWork, Almost Periodic Functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Almost Periodic Functions
Context triple: [Harald Bohr, hasWork, Almost Periodic Functions]
  • A. Tauberian theorems
    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.
  • B. Du Bois-Reymond function
    The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
  • C. The Fourier Integral and Certain of Its Applications
    The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
  • D. 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.
  • E. Asymptotic Methods in Analysis
    Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Almost Periodic Functions
Triple: [Harald Bohr, hasWork, Almost Periodic Functions]
Generated description
Almost Periodic Functions is a foundational mathematical work by Harald Bohr that develops the theory of functions whose values recur with arbitrary precision over time, generalizing the concept of periodicity.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Almost Periodic Functions
Target entity description: Almost Periodic Functions is a foundational mathematical work by Harald Bohr that develops the theory of functions whose values recur with arbitrary precision over time, generalizing the concept of periodicity.
  • A. Tauberian theorems
    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.
  • B. Du Bois-Reymond function
    The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
  • C. The Fourier Integral and Certain of Its Applications
    The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
  • D. 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.
  • E. Asymptotic Methods in Analysis
    Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
  • F. None of above. chosen

Provenance (5 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_69bd4435c2f48190be593158cbfcf8a3 completed March 20, 2026, 12:57 p.m.
NER Named-entity recognition batch_69bd7342c62881909acb35849da8761c completed March 20, 2026, 4:18 p.m.
NED1 Entity disambiguation (via context triple) batch_69be927bdfa481908a5face7b4fd7058 completed March 21, 2026, 12:43 p.m.
NEDg Description generation batch_69be93e00fc08190a0706dd7375020f5 completed March 21, 2026, 12:49 p.m.
NED2 Entity disambiguation (via description) batch_69be94a7e15481908f17feafb593b97b completed March 21, 2026, 12:52 p.m.
Created at: March 20, 2026, 1:35 p.m.