Triple

T5425727
Position Surface form Disambiguated ID Type / Status
Subject Banach inverse mapping theorem E121357 entity
Predicate instanceOf P0 FINISHED
Object theorem in functional analysis of Banach spaces C15242 CONCEPT FINISHED

How this triple was built (1 step)

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.

CD Concept disambiguation gpt-5-mini-2025-08-07
Target class: theorem in functional analysis of Banach spaces
Context triple: [Banach inverse mapping theorem, instanceOf, theorem in functional analysis of Banach spaces]
  • A. functional analysis result chosen
    A functional analysis result is a formal conclusion or theorem that characterizes the behavior, structure, or properties of functions and operators on infinite-dimensional spaces, typically within the framework of normed, Banach, or Hilbert spaces.
  • B. mathematical theorem
    A mathematical theorem is a rigorously proven statement derived from axioms and previously established results, expressing a fundamental truth within a formal mathematical system.
  • C. area of harmonic analysis
    An area of harmonic analysis is a branch of mathematics focused on representing functions or signals as superpositions of basic waves and studying the properties of these representations.
  • D. stability concept in functional equations
    A stability concept in functional equations studies how small deviations from an exact functional relationship affect the existence and form of nearby exact solutions, typically quantifying when approximate solutions imply true solutions close in some specified sense.
  • E. result in real analysis
    In real analysis, a result is a proven mathematical statement—such as a theorem, lemma, proposition, or corollary—that establishes a specific property or relationship about real-valued functions, sequences, sets, or structures on the real numbers.
  • F. None of above.

Provenance (1 batch)

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_69bd463b58d88190b258261573de9e91 completed March 20, 2026, 1:06 p.m.
Created at: March 20, 2026, 2:06 p.m.