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.