Calculate a shortest-arc midpoint composite

Shortest-arc midpoint composite. Antipodal/near-antipodal points reject; no arbitrary flip. Houses are synthetic Equal/Whole Sign from midpoint Ascendant, not physical geographic cusps. Not a Davison chart; no Placidus, node, speed or interpretation option. All admitted attempts use one standard quota unit, including free plans. No practitioner sign-off is claimed.

Each admitted request reserves one monthly usage unit before route validation or engine work; failed or timed-out admitted attempts are not refunded. Do not automatically retry. Historical mode uses an explicit BCE/CE date object and UT1 conventions. Its response is the versioned historical envelope, not the modern UTC envelope. Read result for calculation fields and metadata for limits and uncertainty.