The Witness has many mysterious Collectibles that include well guarded Briefcases scattered about the island.
These briefcases are often found in sealed vaults built into the island, which are locked by imposing steel doors with challenging puzzle panels. Once unlocked, the briefcase will unfold to reveal a puzzle diagram that can be used to unlock special videos in the Underground A/V Room at the Windmill.
Once you've gone beneath the Windmill, you'll find a theater room with corresponding puzzles that match the ones found in the briefcase - each solution will show you a different video.
Below you will find a list of log locations, along with a brief description of its contents - sorted by area.
Briefcase Vault Locations
Entry Area Vault (video 1)
Just after leaving the Entry Area's main gate, look to your left as you head down the path to find a vault carved into the hill. Solve the puzzle on the door to find the briefcase within and get the blueprints.
Desert Ruins Vault (video 2)
If you walk past the Desert Ruins towards the ocean you'll find a stone staircase which leads to a small beach. There you will find the second vault door. On the door there is a tetris & negative block puzzle. Solve the puzzle and go on inside for the briefcase.
Monastery Vault (video 3)
Just behind the Monastery's Zen Garden is a small underground vault blocked by a large puzzle door. To find the solution to this puzzle: turn around and take your first right, then another right, where you'll come upon a root system. Look through it from the right angle---using the negative space to form a stencil---in order to reveal the correct path. Inside the vault you'll find a briefcase with the next diagram.
Caves Vault (Challenge Vault) (video 4)
In order to get this briefcase you need to complete the game. Once you have done so, you'll then be able to reach the bottom of the mountain where you can access The Challenge; otherwise known as "The Music Box" challenge. The reward for completing this challenge is the 4th video solution as well as the platinum trophy on the PS4.
Shipwreck Vault (Keep Vault) (video 5)
The next vault is aboard the Shipwreck. The shipwreck is accessible from the Keep. If you walk through to the back of the Keep, past the floor mazes towards the left tower, you'll find a doorway. This doorway leads to a hole in the wall with a metal walkway leading to the Shipwreck. Make your way to the stern towards the cabin and go downstairs -- there you will find the vault door.
Mountain Vault (video 6)
As you scale the Mountain towards the destination of all the rays of light you'll go past the Greenhouse, a large statue of a woman, and as you continue up you'll see an entrance in the side of the mountain. At the end of this white stairwell is a vault door. Solve the puzzle on the door and go inside for the briefcase.