R-layer Mode Theory Volume I: Projection, Stability, and Higher‑Layer Dynamics

This Volume I extends the R‑layer Mode Theory (RLMT) by developing its dynamical and mathematical foundation. Four‑dimensional spacetime is treated as a projection of a higher‑dimensional information manifold, where matter (MUP) and antimatter (AUP) arise as distinct projection states of a single higher‑layer structure. We introduce a projection operator linking the higher‑layer manifold to 4D spacetime, define fiber structures associated with each 4D point, and derive effective potentials governing mode stability. Information flow equations describe projection, uplift, mixing, and reprojection between layers, while quantum entanglement is reinterpreted as a manifestation of inter‑layer connectivity. The volume formulates torsion‑based amplification of asymmetry, mode conversion between AUP and MUP, and the geometric conditions for stabilizing projection modes. A conceptual AUP‑based detector is proposed as a possible gateway to probe higher‑layer geometry, suggesting that higher‑dimensional physics may be experimentally accessible in principle. Together with Volume 0, this work establishes the mathematical core of RLMT and lays the groundwork for future volumes on tensor perturbations, entanglement wedges, and cosmological applications.