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Applications

This is also yet very incomplete
The main idea here is that the browser is the OS for applications.  In a P2P network, you don't have servers which perform the applications, and "lightweight" terminals which just display the result.  You need to distribute the programs just like any other object.  The main purpose for applications is to display content.
Content is (structured) text, images, videos, music, etc.

Turing creep

There's a phenomenon I call "Turing creep": Any environment strives to become Turing complete, i.e. it will in the long run contain a Turing complete language, accessible by the user.  Even if you try to remove the Turing completeness (like in PDF, the predecessor PostScript was TC), it will creep in through the backdoor (PDF has now JavaScript macros).
Therefore, you better start with a Turing complete language. To be more precise: An efficient TC language.  People will otherwise spend an enormous amount to make the inefficient language efficient, or add an efficient subset (see for example JavaScript and asm.js).
This of course begs the question of security: How can you securely execute code that comes from the Internet?

Secure execution

The following options have been tried, and some of them failed more spectacularly than others:
  1. Execute code in a controlled VM (e.g. Java).  This is broken by design, you can't secure something from the inside.
  2. Execute code in a sandbox.  This has been shown to be way more robust; it is much harder to break out of a sandbox.
  3. Public inspection of code: This is the free software approach.  The underhanded C context shows that public inspection is tricky.  Especially large code bases are problematic.
  4. Scan for known evil.  This is the security industry's approach, and it is broken.
  5. Code signing is also a scam - it can work together with public inspection, but using it for accountability doesn't work.
Therefore the method of choice is to execute public inspected and signed code in a sandbox (signed by the inspectors is the important part).

Output Abstraction

The low-level output abstraction (least common denominator) available on today's platforms is OpenGL ES 2.0.  Yes, there is Windows Phone, which has essentially the same capabilities, but not the same framework.  All relevant data can be rendered using OpenGL: Fonts, images, videos are OpenGL textures, the glue for displaying these textures are triangles and GL shader language code.  This can provable display everything we want to display today.

Frameworks used