Calculate Moon phase geometry or a bounded primary-phase calendar

Explicit instant mode returns a named display sector, Moon-minus-Sun ecliptic longitude and separately calculated spherical illuminated fraction. Calendar mode returns primary longitude crossings, not eclipse predictions or visibility. Dates 1800–2200; calendar spans at most 366 UTC days. No coordinates, zodiac, user kernels or arbitrary search tuning. Uses existing DE440 and bundled time-scale data; future UTC assumes the bundled leap-second schedule. Current: one-second output and millisecond root convergence are not accuracy guarantees. Independent 2026 USNO comparison has a 60-second tolerance; broader epoch/time-scale acceptance remains separate. Each admitted request reserves one standard monthly quota unit, including invalid inputs and timeouts. All plans; no automatic retries. Source availability does not establish deployment. 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.