The Shoreditch Library was the main library in Shoreditch, London. The First Doctor registered there sometime between May and November 1963. (TV: The Vampires of Venice, An Unearthly Child)
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The Doctor's library card
His registration represents the Doctor's earliest (from his perspective) known use of the John Smith alias, and was concurrent with the Hon. Aubrey Waites' use of the same pseudonym. (TV: An Unearthly Child)