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.