Documented: the Calendar of Philocalus (354 CE) marks December 25 as N Invicti, the games of the Unconquered Sun instituted under Aurelian (274 CE), and the same codex's martyrology opens the year with Christ born in Bethlehem on December 25, the earliest Western record of Christmas. The competing scholarly explanations are both documented: substitution theory, the church supplanting the solar festival, and calculation theory, Christ conceived March 25, his crucifixion date, and born nine months later, a documented patristic logic.
The folk reading, Maxwell's lecture: the sun dies on the cross of the solstice, rests three days at its lowest, and is reborn on the 25th, so the solar hero's biography is written in the sky and every December the church performs astronomy without a license. The Saturnalia week, gift-giving, role reversal, feast, supplies the customs.
The claim: the shared birthday is the visible seam where the sky religion and the book religion signed their merger, and the persistence of the date through every reform is the signature of the older partner. The counter: dates converge because the solstice is the one holiday the planet itself enforces.
Did the church copy the sun's birthday, or did both calendars simply aim at the solstice?