Triple
T13444243
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Paul Halmos |
E320438
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Introduction to Hilbert Space and the Theory of Spectral Multiplicity
"Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
|
E1041773
|
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: Introduction to Hilbert Space and the Theory of Spectral Multiplicity | Statement: [Paul Halmos, notableWork, Introduction to Hilbert Space and the Theory of Spectral Multiplicity]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Introduction to Hilbert Space and the Theory of Spectral Multiplicity Context triple: [Paul Halmos, notableWork, Introduction to Hilbert Space and the Theory of Spectral Multiplicity]
-
A.
Les algèbres d’opérateurs dans l’espace hilbertien
Les algèbres d’opérateurs dans l’espace hilbertien is a foundational monograph by Jacques Dixmier that systematically develops the theory of operator algebras on Hilbert spaces, particularly C*-algebras and von Neumann algebras.
-
B.
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.
-
C.
Introduction to Abstract Harmonic Analysis
Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
-
D.
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.
-
E.
Harmonic Analysis and the Theory of Probability
Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability 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: Introduction to Hilbert Space and the Theory of Spectral Multiplicity Triple: [Paul Halmos, notableWork, Introduction to Hilbert Space and the Theory of Spectral Multiplicity]
Generated description
"Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Introduction to Hilbert Space and the Theory of Spectral Multiplicity Target entity description: "Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
-
A.
Les algèbres d’opérateurs dans l’espace hilbertien
Les algèbres d’opérateurs dans l’espace hilbertien is a foundational monograph by Jacques Dixmier that systematically develops the theory of operator algebras on Hilbert spaces, particularly C*-algebras and von Neumann algebras.
-
B.
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.
-
C.
Introduction to Abstract Harmonic Analysis
Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
-
D.
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.
-
E.
Harmonic Analysis and the Theory of Probability
Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability 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_69d80761e6cc8190a90c844589998ecc |
completed | April 9, 2026, 8:09 p.m. |
| NER | Named-entity recognition | batch_69dbaee881888190811ddf01bc699864 |
completed | April 12, 2026, 2:40 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f739965ef081909e85881ce805bbb5 |
completed | May 3, 2026, 12:03 p.m. |
| NEDg | Description generation | batch_69f740e536d48190af369b38aa42438d |
completed | May 3, 2026, 12:34 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69f741b72d08819087808bf9bcffa0a1 |
completed | May 3, 2026, 12:38 p.m. |
Created at: April 9, 2026, 9:40 p.m.