Write latex comments on any pdf file with option to toggle comments on and off

I am looking to take a .pdf file (for example an Arxiv paper), and add math comments using Latex / Markdown synatx onto the pdf with the option to toggle the comments on and off.

More precisely, consider for example this pdf file http://wwwf.imperial.ac.uk/~pavl/stoch_proc_notes-ch1-3.pdf . Suppose on page 15 of the document I want to add a note to Example 2.21. More specifically i want to add the following math comment (using latex) $f_X(x) \in \mathbb{E}$ beside the equation in colored text.

If this comment was not mathematical (i.e. just text) , I would be able to easily add it using a pdf reader such as Preview or Adobe acrobatic reader. However, I see no option as to how one can easily add math comments to pdfs.

Furthermore, both preview and acrobat have features where one can toggle the view of all the comments added to the pdf on and off, (which would be very useful when reading).

Solution

For complex math formulas you cannot generally use simple text based annotation/comments. In your requested example the top two comments were added by readers as plain text and the conversion is problematic since annotation often has poor support for math unless a few more common/basic symbols like Greek letters.

Plain LaTeX notes would need the PDF to be overstamped

However Editor level viewers can easily add stamped Mathematical PDF rendering such as this using Tracker PDF XChange, given the correct input (the stamp was produced compliments of https://latex.codecogs.com/). and you should be able to scale /colour this snippet as SVG or produce PNG / PDF for insertion or cut and paste to typewriter or if more complex then stamp as an image.

<body><img src="https://latex.codecogs.com/svg.image?\inline&space;f_X(x)&space;\in&space;\mathbb{E}" title="\inline f_X(x) \in \mathbb{E}" /></body>