Calculate explicit Pythagorean numerology arithmetic

Symbolic calculation-only numerology: component-wise birth-date reduction, optional ASCII-name sums and an explicitly requested calendar-year cycle. Includes reduction traces, exact master-number and Y conventions. No interpretation, scientifically validated prediction, personality assessment or advice. Name data is not persisted by this route; use only data you are authorized to process. Each admitted request reserves one standard monthly unit; failed or timed-out admitted attempts are not refunded. Not a durable-job operation. 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.