The Solstice-Sirius Coincidence as a Latitude-Indexed Calendrical Anchor

The heliacal rising of Sirius and the June solstice are governed by different years. The star returns on the sidereal year, the solstice on the tropical year, and the two differ by about twenty minutes, so the interval between the two events migrates through the calendar and the two coincide only once in a precessional cycle. This paper computes when that coincidence occurred, and reports that it is not a single date but a latitude-indexed family of dates: because the heliacal rising depends on the observer's latitude and the solstice does not, the coincidence falls at systematically different epochs at different latitudes, at a rate of roughly 124 years per degree. Computed with full stellar space motion and a long-term precession model, the coincidence falls at 710 BCE and 26,416 BCE for latitude 11.87 degrees north, at 2,615 BCE and 27,719 BCE for the latitude of Giza, and at 3,335 BCE for Baalbek. Above approximately 37 degrees north no recent solution exists. The dominant uncertainty is the visibility threshold, which displaces the epochs by about 100 years at low latitude and about 165 years at the latitude of Giza. A corollary is developed: because the same drift is measurable as a shift of roughly one day per century in the interval between the two events, precession is recoverable from calendar records alone, without any observation of a pole star, given records spanning several centuries. No claim is made that any culture performed this measurement; the paper establishes when the coincidences occurred, how precisely they can be dated, and what would be required to have detected the underlying drift.