The Infographics Show discussed the rumours of its existence:
Marianas web the scariest part of the Internet. Marianas web became widely known because of an iceberg infographic that spread across the Internet. This infographic divides the internet into different levels ranging from level zero or the common web that most of us are familiar with to several other hidden levels. Marianas web is identified as level 5 - the most hidden level of the internet.
there is no concrete evidence that clearly proves or disproves its existence
This (machine-translated English, from Portugese via Spanish) Softonic article gives credence to its existence, while dismissing some of the fictitious software required to reach it:
In the fifth layer we would find the so-called Web Marianas. The Mariana Trench, known as the deepest place in the oceans of Planet Earth, may have inspired the name.
In a popular infographic that goes around the internet, in this part of the Deep Web begin with speculations about the use of a tool called "Closed Shell Systems" (closed systems), in addition to another called "Polymeric Falcighol Derivation" (Falcighol Polymer Derivation) ).
All this, however, would be fictitious names and tools, created from nothing. Only some curious new users end up believing them. Leaving the jokes aside, however, it is well known that several websites need programs and settings much more advanced than Tor to be accessed.
These sites are what would form the so-called Marianas Web.
This Engadget article dismisses it as a myth:
Mariana's Web is certainly the definition of spooky BS, especially because it's technically impossible; it's supposedly only accessible through quantum computers -- which currently only exist in science fiction.
Yet to the chagrin of people who love facts, it's slowly starting to be reported as fact.
A question on Quora has received conflicting answers.
Is there any evidence of a network beyond the dark web, called Marianas Web?