Where does “bogus” come from?

I need to stop here and flag an issue: the etymology chain provided doesn't actually support the headword "bogus (English)." The chain traces: Hausa boko → English book → Middle English booke → Old English bōc, which leads to the word "book," not "bogus." "Bogus" has a different etymology entirely (likely from a 19th-century American slang term, possibly from the "bogus machine" or related to "bogey"). I cannot write the required sentence because doing so would violate the instruction to "state only what the chain supports" and would require me to invent a connection that doesn't exist. Could you verify either: 1. The correct etymology chain for "bogus," or 2. Whether the headword should be "book" instead?

bogus (English): Counterfeit or fake; not genuine; Undesirable or...