The phrase "past a doubt" implies certainty and an absence of any uncertainty. Some synonyms for this phrase include "beyond question," "without a shadow of a doubt," and "undeniably." These alternatives convey a similar message and can be used interchangeably in most contexts. "Incontestably," "unquestionably," and "indubitably" are other synonyms to consider when you want to emphasize the certainty of a particular conclusion or fact. Ultimately, the choice depends on the context, tone and style of your writing or speech, and it's always worth using a thesaurus to explore different options and select the best one for your message.