Final answer is
or perhaps I should say
I confess that I only bothered going this far by strict logical inference
before allowing myself to make the obvious assumptions about the structure of the solution, leading to this (where white and yellow should now be treated as equivalent):
whereupon it's clear how to get to the solution at the top.
(I did this without looking at the CW. I claim no credit for imposing arbitrary restrictions on myself, but it means any mistakes are my own :-).)
The final grid is as follows:
which obeys the following constraint:
If we interpret
"First", "Second", etc., are of course
When groups of cells are referred to collectively,
Note: in the course of ...
The grid looks like a game of Descartes Enigma - perhaps that's where you found it on your computer?
The numbers labelling each row and column give the pattern of black cells in each row or column; different numbers correspond to groups of black cells which must have white cells in between.
The grid is $15\times21$, so we can fill in a few sets of black ...