The Ascendant is not a meridian. At each latitude φ the hour angle of rising solves cos H = −tan φ tan δ, so the terrestrial line bends as latitude changes.
The curve stops where the planet never crosses the horizon: |φ| > 90° − |δ|. Meridian leaves that endpoint open instead of drawing a fictitious bridge to the pole.
Each mathematical solution is checked by azimuth. The eastern horizon is ASC and the western horizon is DSC, avoiding the longitude and hour-angle sign mistakes that easily mirror a map.