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Preheat oven to 350 degrees.
Snap off and discard the tough ends of asparagus. Bring a medium saucepan of salted water to a boil; prepare an ice bath. Cook asparagus until bright green and just tender, 2 to 3 minutes. Transfer immediately to ice bath. Drain; place on a clean kitchen towel.
Spread torn bread on a baking sheet drizzle with olive oil and bake in the oven until lightly toasted.
In a large bowl, combine asparagus, radishes, tomatoes, red onion, arugula, and bread; toss to combine. In a small bowl, whisk together red-wine vinegar and olive oil; season with salt and pepper. Pour vinaigrette over asparagus mixture, and toss until well coated. Let sit until bread absorbs juices, and serve.