Special equipment: a mandoline or other manual slicer, 4 pieces parchment paper, kitchen string
Preheat oven to 400 degrees F.
Halve fennel bulb lengthwise. Remove most of core, leaving enough intact to keep layers together when sliced.
Using manual slicer, cut fennel bulb (lengthwise), carrots (diagonally), and potatoes into 1/8-inch-thick slices, keeping vegetables separate.
Blanch vegetables, separately, in salted boiling water: fennel 2 minutes, carrots 1 minute, potatoes 2 minutes. Transfer fennel and carrots with a slotted spoon to a bowl of ice water then drain well. Drain potatoes.
Toss fennel and carrots with olives, zest, thyme, half of garlic, 2 tablespoons olive oil, and salt and pepper, to taste.
Toss potatoes with remaining oil and garlic and salt and pepper, to taste.
Fold the parchment paper in half along the longest side. Divide potato mixture among centers of parchment squares. Season salmon with salt and pepper and place on top of potatoes, then top salmon the fennel mixture. Add a pat of butter to the package and a squeeze of lemon juice.
Fold the parchment paper up over fennel mixture and crimp the edges. Place packages directly on hot baking sheet in oven and cook 20 minutes. Serve immediately.
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