Cotangent-compensated Cayley maps v1.0.0

First public archival preprint release.\n\nThis release contains:\n- the six-page mathematical preprint;\n- canonical LaTeX source;\n- exact SymPy verification for a generic n=2, K=2 representative;\n- recorded expected output and verification environment;\n- SHA-256 supplement integrity manifest; and\n- the focused literature audit dated 2026-08-21.\n\nThe manuscript and documentation are licensed under CC BY 4.0. Verification software and repository tooling are licensed under BSD-3-Clause.\n\nThe result is deliberately narrow and is presented as an explicit specialization of established generating-function and cotangent-lift machinery. This release has not been peer reviewed.