Audit chart sensitivity to birth-coordinate precision

Calculates one exact birth moment at the supplied coordinates and eight equally spaced bearings on a caller-declared spherical radius. It reports selected-planet house stability, explicit per-sample geometry failures, and maximum Ascendant, Midheaven, and cusp displacement from the center for one selected 12-house system. The nine samples describe only the center and perimeter points; they are not statistical confidence, do not guarantee every point inside the disk, and do not rank locations, rectify birth data, interpret a chart, or make predictions. Gauquelin is excluded because it is a 36-sector system. One standard quota unit per admitted request; 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.