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You can only enter into a common law marriage very few jurisdictions in the US and certainly not in California. In jurisdictions where you can legally enter into common law marriage in the US, the couple doesn't just "get married" by cohabitation for a few years, they have to actually agree to get married and present themselves as married to others. It's very clear that they must want to be married and agree to be married. It usually requires a public decoration of marriage. (So a marriage ceremony, just without an officiate)

You can also file married income taxes if you are legally married in your state of residence. In fact, if you didn't it probably would be considered tax fraud.