Extreme tier Technique 29 of 31 Used by Smart Hint

Connectivity

The finished loop is a single connected shape, so every line already drawn has to end up joined to every other one. An edge marooned in a pocket the drawn lines can never reach is ruled out.

How it works

1The finished loop is ONE closed shape, and it can only travel along edges you have not ruled out — so every X on the board is a wall, and the question worth asking is where the loop can still physically get to.
2Follow the walls around the top-left cell. Its four sides are all still open, but every route out of them is crossed off, so those four edges form a pocket the loop could only ever enter by starting inside it.
3A line is already drawn over on the right, and the loop has to pass through there — it cannot also be a separate ring in the corner.
4So the pocket is dead: cross off its top edge, and the dot rule will take the other three. Connectivity deductions must still respect that the answer is a cycle: a one-edge bottleneck is impossible, because a closed loop cannot cross a cut only once.

Edge on the loop
Edge ruled out
Cells that establish the pattern

Next in the ladder Region Coloring →

Shading every cell as inside or outside the loop (with the space beyond the grid always outside): a line always separates two different shades, a blank always keeps the same shade. Chaining that logic across the board pins down edges too far apart for any single clue to reach alone.