The figure of 1461 is, as you explain, the number of years for Sirius to rise heliacally again on the New Year's day.

But it is also the number of days in a four year cycle of 365 + 365 + 365 + 366 days, one of which is the Leap year. (This is of course the cycle for the sunrise to match the stars again.)

One of the jobs of the ascended King was to maintain cosmic order, or Maat, in which the sun and stars follow their prescribed cycles.

The tool to do this is maybe in plain sight at Giza and the number of 1461 is there.

The so-called workman's barracks sits symmetrically behind Khafre's pyramid.

There are 73 North-South galleries and 20 East-West galleries.

Days can be counted if each E-W gallery is worth 73.

20 x 73 is 1460.

But there is one extra gallery built separately at the top of the 73.
If this is used once per cycle we have 1461.

This idea I posted 4 years ago :

[www.hallofmaat.com]