This is a Heyacrazy* puzzle. The rules are as follows:

• Shade in some cells in the grid. Two shaded cells cannot share an edge, and all unshaded cells must be orthogonally connected.
• Once finished, it is not possible to draw a line segment in the grid which passes through two borders (bolded lines) without passing through a shaded cell.

* Heyacrazy is a puzzle type created by Deusovi[1] based on Nikoli's Heyawake.

• Ha, I literally only just realised that the line segments in the centre of this puzzle spell out JAFE upside down! Slow moment...
– Stiv
Dec 14, 2022 at 10:16

Solution:

Explanation:

The first step is to recognize that the v in the middle must be shaded in one of 2 ways, either
or
.

However, if we progress down the first option, we will eventually reach this state: ,
which would require us to shade 2 adjacent boxes to prevent any lines.

Thus, the correct start must thus be the second option.

From there we can fill out most of the grid via application of the rules until we reach this state:

Where we find this situation:

One of the red or purple needs to be filled out, and one of the blue and purple needs to be filled out.

However, if we fill out the red and the blue, we will end up in this situation:

Where we can't fill in any of the red squares without breaking the continuous unshaded rule.

Thus, we must fill in the purple square, and from there the final few squares are straightforward, giving us a final state of: