Actually, you can. Browsers don't care about docs. HTML 4 strict or HTML 5 won't make any difference, just make sure your page is in standard mode and not Quirks mode .
Personally, I see no reason not to use the HTML5 doctrine, since you will use HTML5, and, unlike any other, you can remember this!
Of course, the session store defined in HTML5 will not work in IE6, but it is up to you to decide which reserve you will provide.
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