R-layer Mode Theory (RLMT) XLI‑K: Observational Information Flow Across Scales

This volume extends R-layer Mode Theory (RLMT) to observational contexts across multiple physical scales, including supernova remnants (SNRs), black hole environments, and cosmology. We formulate R-layer information-flow equations for each setting, define reduced density matrices adapted to observational surfaces, and relate R-layer entanglement currents to measurable quantities such as X-ray luminosity, black hole radiation entropy, and cosmological mode entanglement. A unified information-flow equation, dS_obs/dt = F_out − F_in, emerges across all systems, providing a common structure behind Page-like transitions in SNRs, black holes, and cosmology. The framework suggests a program for constraining RLMT parameters using multi-scale observational data.