Transport and Projective Reduction in a Source–Readout Derivation of Einstein Gravity

This paper presents a complete conditional source–readout realization of Deser’s massless spin-two self-coupling derivation, recovering the full nonlinear Einstein–matter equations within Shadow Theory’s source-to-readout architecture. The construction explicitly defines the admitted source support, preparation, physical transport variables, projection maps and inverse reconstruction. It preserves the variational operations and stress response needed for the gravitational bootstrap, rather than identifying only its final equations. The paper establishes several connected results: Smooth multiplicative transport yields a local affine connection under explicit regularity assumptions, with quantitative reconstruction and error bounds. An unrestricted affine parent removes the need to impose torsion-free kinematics initially. Its connection equations and a volume-restored projective readout recover Levi–Civita transport. An explicit off-shell stress formula and residual identity preserve the derivative self-current and complete the cubic bootstrap. Metric and matter variations recover the nonlinear Einstein–matter equations with consistent coupling normalization. A dependency analysis distinguishes source-derived structure, conditional assumption reductions and remaining physical inputs, supported by explicit competing realizations. The result provides a complete mathematical realization of the selected gravitational derivation. Selection of dimension, Lorentzian signature, the starting gravitational law and coupling from source principles alone remains a further research problem. The accompanying public verification package contains executable code, specifications, saved outputs, generated tables, dependency versions, integrity hashes and reproduction instructions. Verification includes 99 scientific checks and three software portability regressions, with successful Windows and Linux replay. Author: Jeremy Rodgers, Independent ResearcherWebsite: https://everythingequation.comDOI: https://doi.org/10.5281/zenodo.23954887