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.