But the text supports Branagh. In the soliloquy "Oh, that this too too solid flesh ... " Hamlet chides his mother for marrying his uncle "within a month" of her first husband's death, going on to make clear he was talking about February - "A little month". Ergo, the old king was done in at the end of January.
Mind you, his fondness for sleeping outdoors in the Danish winter makes one wonder whether Hamlet senior might not have been a few kroner short of a smorgasbord and why anybody should have given any credence to his ghost. But that's literature for you.
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