Triple
T4219668
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Stefan Banach |
E94307
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Theory of Linear Operations
Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
|
E421064
|
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: Theory of Linear Operations | Statement: [Stefan Banach, notableWork, Theory of Linear Operations]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Theory of Linear Operations Context triple: [Stefan Banach, notableWork, Theory of Linear Operations]
-
A.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
-
B.
Produits tensoriels topologiques et espaces nucléaires
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
-
C.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
D.
Lectures on Cauchy’s problem in linear partial differential equations
"Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
-
E.
Generalized Functions (multi-volume series)
Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
- 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: Theory of Linear Operations Triple: [Stefan Banach, notableWork, Theory of Linear Operations]
Generated description
Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Theory of Linear Operations Target entity description: Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
-
A.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
-
B.
Produits tensoriels topologiques et espaces nucléaires
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
-
C.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
D.
Lectures on Cauchy’s problem in linear partial differential equations
"Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
-
E.
Generalized Functions (multi-volume series)
Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
- 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_69b3451997e08190851db4a9a588837d |
completed | March 12, 2026, 10:58 p.m. |
| NER | Named-entity recognition | batch_69b34e0b2ee08190930600e1e802b325 |
completed | March 12, 2026, 11:36 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b5963ffacc8190843b60ea1b224f91 |
completed | March 14, 2026, 5:09 p.m. |
| NEDg | Description generation | batch_69b596b7330081908c66a5a756531ffd |
completed | March 14, 2026, 5:11 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69b5976663d88190a73a729554e91074 |
completed | March 14, 2026, 5:14 p.m. |
Created at: March 12, 2026, 11:04 p.m.