Dirac-to-Tensor-Curl Eta Transfer on Round Spherical Space Forms with Affine-ADE Specializations

A representation-theoretic transfer from flat-twisted spin-Dirac eta data to projected integer-rank tensor-curl invariants on round spherical space forms. Closed cyclic and binary-dihedral formulas, exceptional-family source recurrences, and two-sided lens and nonabelian direct-product examples are given. Operator, spin-lift, multiplicity and orientation conventions are explicit. AI-assisted research, computation, checking, and editorial support used OpenAI Codex and Anthropic Claude. Luqman Mahmood directed the research and is responsible for the claims and final text. Automated and internal checks are not external peer review. CC BY 4.0 covers the scholarly documents and mathematical data. Software is excluded from that grant; see LICENSE.md.