Spectral chirality of lens spaces: level-wise helicity balance, eta congruences, and silver zeros for transverse-traceless tensor curl

Results for the projected transverse-traceless tensor-curl family on oriented lens spaces, including helicity balance, eta congruences, and connections to silver-rank zeros. Operator and orientation conventions are explicit; no physical identification is inferred. AI-assisted research, computation, checking and editing used OpenAI Codex and Anthropic Claude. Luqman Mahmood directed the research and is responsible for its claims and final text. Internal checks are not external peer review or an establishment of priority. CC BY 4.0 covers scholarly documents and mathematical data. Software source and executable verification scripts are excluded; their rights remain reserved unless an individual file states otherwise. Proprietary engineering implementations are not included.