Triple

T2866511
Position Surface form Disambiguated ID Type / Status
Subject Princeton Mathematical Series E63452 entity
Predicate workIncluded P10663 FINISHED
Object "Functional Analysis"
Functional Analysis is a branch of mathematical analysis that studies vector spaces with additional structure (such as norms and inner products) and the linear operators acting on them, with deep applications across pure and applied mathematics.
E305927 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: "Functional Analysis" | Statement: [Princeton Mathematical Series, workIncluded, "Functional Analysis"]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: "Functional Analysis"
Context triple: [Princeton Mathematical Series, workIncluded, "Functional Analysis"]
  • A. Banach spaces
    Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
  • B. Hilbert spaces
    Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
  • 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. Asymptotic Methods in Analysis
    Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
  • 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: "Functional Analysis"
Triple: [Princeton Mathematical Series, workIncluded, "Functional Analysis"]
Generated description
Functional Analysis is a branch of mathematical analysis that studies vector spaces with additional structure (such as norms and inner products) and the linear operators acting on them, with deep applications across pure and applied mathematics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: "Functional Analysis"
Target entity description: Functional Analysis is a branch of mathematical analysis that studies vector spaces with additional structure (such as norms and inner products) and the linear operators acting on them, with deep applications across pure and applied mathematics.
  • A. Banach spaces
    Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
  • B. Hilbert spaces
    Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
  • 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. Asymptotic Methods in Analysis
    Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
  • 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_69ab4c42fb8c8190b36e161d47c03b81 completed March 6, 2026, 9:50 p.m.
NER Named-entity recognition batch_69abe08c85c48190bd8c0f6680fca0c8 completed March 7, 2026, 8:23 a.m.
NED1 Entity disambiguation (via context triple) batch_69b01da85930819092d19a5e712cfa18 completed March 10, 2026, 1:33 p.m.
NEDg Description generation batch_69b01e34639c8190b1c6e8a14cd31d96 completed March 10, 2026, 1:35 p.m.
NED2 Entity disambiguation (via description) batch_69b01f5a6784819089499926fb115d9c completed March 10, 2026, 1:40 p.m.
Created at: March 6, 2026, 10:02 p.m.