Triple

T11085785
Position Surface form Disambiguated ID Type / Status
Subject Voronin universality theorem E262116 entity
Predicate relatedTo P37 FINISHED
Object Bohr–Courant theorem
The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
E904000 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: Bohr–Courant theorem | Statement: [Voronin universality theorem, relatedTo, Bohr–Courant theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bohr–Courant theorem
Context triple: [Voronin universality theorem, relatedTo, Bohr–Courant theorem]
  • A. Courant–Fischer min–max theorem
    The Courant–Fischer min–max theorem is a fundamental result in linear algebra and spectral theory that characterizes the eigenvalues of a Hermitian (or symmetric) matrix via variational min–max principles over subspaces.
  • B. Bose–Nair theorem
    The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
  • C. Bogoliubov–Parasyuk theorem
    The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
  • D. Paley–Wiener theorem
    The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
  • E. Bernstein theorem
    Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
  • 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: Bohr–Courant theorem
Triple: [Voronin universality theorem, relatedTo, Bohr–Courant theorem]
Generated description
The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bohr–Courant theorem
Target entity description: The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
  • A. Courant–Fischer min–max theorem
    The Courant–Fischer min–max theorem is a fundamental result in linear algebra and spectral theory that characterizes the eigenvalues of a Hermitian (or symmetric) matrix via variational min–max principles over subspaces.
  • B. Bose–Nair theorem
    The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
  • C. Bogoliubov–Parasyuk theorem
    The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
  • D. Paley–Wiener theorem
    The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
  • E. Bernstein theorem
    Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
  • 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_69d6aa9983c08190b0ef61603b69feac completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d799c2c7d4819087ac793153340178 completed April 9, 2026, 12:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69e3e7a6dfa8819096f822294eb64dd1 completed April 18, 2026, 8:20 p.m.
NEDg Description generation batch_69e3f2cafc008190a3504999297f1e4e completed April 18, 2026, 9:08 p.m.
NED2 Entity disambiguation (via description) batch_69e3f488819081908f9a4225279cde6b completed April 18, 2026, 9:15 p.m.
Created at: April 8, 2026, 9:27 p.m.