In a stockpot over medium heat, combine cobs and 7 cups water, and simmer for 30 minutes. Remove cobs with tongs and discard; reserve stock.
In a stockpot over medium heat, cook bacon, stirring often, until cooked through but not crisp. Transfer to a paper-towel-lined plate. Add sweet potato, onion, and butter to pot. Season with 1/2 teaspoon salt and cook until potato and onion soften, about 15 minutes. Add garlic and rosemary, and cook for 1 minute. Add corn kernels, 5 cups of reserved corn stock, pepper, and remaining salt, and bring to a simmer.
Transfer half of soup to a blender and puree until smooth. Using a fine-mesh sieve, transfer pureed soup back into stockpot. Stir wild rice and reserved bacon into soup. Serve immediately.
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