"I know I’ve seen fiction where it requires little more than cohabitation, but that’s not a real thing."
New Hampshire: Common Law Marriage: "persons cohabiting and acknowledging each other as husband and wife, and generally reputed to be such, for the period of 3 years, and until the decease of one of them, shall thereafter be deemed to have been legally married." (N.H. Stat. §457:39)
So not really a fiction. There aren't many requirements there.
The old law in PA did not even require habitation or a contract. All that would be required aside from regular eligibility stuff would be presenting themselves in public as husband and wife plus exchanging words of intent at one time to be married (verbal contract). That law was active until as recently as 2005.