Happy Second Of July! In libertarian SF novelist's L. Neil Smith's 1979 alternate history book The Probability Broach, the protagonist visits an alternate reality where they celebrate Independence on the Second of July.

There's a reason for that, he discovers: "July second is the correct date, in both worlds!" He notes that local historians, in his alternate universe, "are just a little more accurate. That's when independence was really declared, at the instigation of Richard Henry Lee and John Adams. The document explaining what they'd done was adopted on the fourth."

This is true, as explained here in the Wall Street Journal:

In early July 1776, John Adams wrote to his wife, Abigail, about a momentous day during the proceedings of the Second Continental Congress in Philadelphia. Adams predicted that the day "will be celebrated by succeeding generations as the great anniversary festival. It ought to be solemnized with pomp and parade, with shows, games, sports, guns, bells, bonfires and illuminations from one end of this Continent to the other from this time forward forever more."

Adams was speaking about the red-letter day when the Continental Congress voted to declare America's independence from Britain. That memorable event – when the United States of America was born – occurred on July 2, 1776. Two days later, a second vote was taken, and 12 of the 13 colonial delegations (New York abstained) once more voted in favor of adopting what would become known as the Declaration of Independence.

The Founding of Fireworks, by Marc Leepson, July 3, 2008

What's amazing is that Adams knew that what they'd started would be celebrated as long as it has. In 2021, the official day off is the Fifth of July, for purposes of a long weekend, but if you find yourselves celebrating today, you're not wrong.