Triple
T11411906
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Mark Naimark |
E270390
|
entity |
| Predicate | hasTheoremNamedAfter |
P29208
|
FINISHED |
| Object |
Naimark problem
The Naimark problem is a question in operator algebra theory concerning whether every C*-algebra with certain representation properties must be of a particularly well-behaved (type I) form.
|
E924211
|
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: Naimark problem | Statement: [Mark Naimark, hasTheoremNamedAfter, Naimark problem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Naimark problem Context triple: [Mark Naimark, hasTheoremNamedAfter, Naimark problem]
-
A.
Steklov eigenvalue problem
The Steklov eigenvalue problem is a type of spectral boundary value problem in which eigenvalues appear in the boundary conditions of a partial differential equation, playing a key role in mathematical physics and geometric analysis.
-
B.
Sturm–Liouville problem
The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
-
C.
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.
-
D.
Dirichlet problem
The Dirichlet problem is a fundamental boundary value problem in potential theory and partial differential equations, asking for a function that solves a specified PDE inside a domain while taking prescribed values on the domain’s boundary.
-
E.
Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
- 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: Naimark problem Triple: [Mark Naimark, hasTheoremNamedAfter, Naimark problem]
Generated description
The Naimark problem is a question in operator algebra theory concerning whether every C*-algebra with certain representation properties must be of a particularly well-behaved (type I) form.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Naimark problem Target entity description: The Naimark problem is a question in operator algebra theory concerning whether every C*-algebra with certain representation properties must be of a particularly well-behaved (type I) form.
-
A.
Steklov eigenvalue problem
The Steklov eigenvalue problem is a type of spectral boundary value problem in which eigenvalues appear in the boundary conditions of a partial differential equation, playing a key role in mathematical physics and geometric analysis.
-
B.
Sturm–Liouville problem
The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
-
C.
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.
-
D.
Dirichlet problem
The Dirichlet problem is a fundamental boundary value problem in potential theory and partial differential equations, asking for a function that solves a specified PDE inside a domain while taking prescribed values on the domain’s boundary.
-
E.
Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
- 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_69d6aaddeaa8819088b30ef7b50598c9 |
completed | April 8, 2026, 7:22 p.m. |
| NER | Named-entity recognition | batch_69d8015017d08190b4020c76545556d6 |
completed | April 9, 2026, 7:43 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e5b855f0508190a2e57ef9407ddb1a |
completed | April 20, 2026, 5:23 a.m. |
| NEDg | Description generation | batch_69e5c28d3824819097ff84cb4e13c923 |
completed | April 20, 2026, 6:07 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e5c451c6c88190bcbb1f54ede35d29 |
completed | April 20, 2026, 6:14 a.m. |
Created at: April 8, 2026, 9:34 p.m.