"The beauty of the American government is that it treats all religions the same, and ideally keeps them at arm's length."
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You are aware, I am sure, that the "date" a "legal document" is signed is a part of that document because, in many cases, the date may become important to determine the legality of the document.
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Ever look at how The Constitution of the United States is dated?
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It's rather "unique"....in today's wording....but was very, very common in 1787....and for years thereafter. 
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Isn't it rather odd that the Constitution that established, as you say, "the beauty of the American government"....is dated in a way that actually does not "treat all religions the same".....but actually refers to Jesus Christ, and Jesus Christ alone, as the one and only possible "our Lord" in the Constitution?
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And, of course, you know that one of the first acts Congress did was to appropriate funds to buy Bibles for public schools. Bibles. For Public Schools. Congress did that.