R-layer Mode Theory (RLMT) XLI‑N: Observational Constraints on Black Hole Physics and Dark Matter in the R-layer Framework

This volume develops the observational component of Phase III of R-layer Mode Theory (RLMT). Building on the Fisher information kernel and quantum information stress tensor introduced in Volume LXXXI, we construct coarse-grained Fisher probes tailored to astrophysical systems across a wide range of scales. Using constraints from primordial black hole non-detection, the M87 jet, quasar spin measurements, galaxy interactions, and protoplanetary disks, we derive quantitative bounds on different projections of the R-layer Fisher kernel. These bounds restrict the induced non-local mass and dissipation kernels, the R-layer corrections to quasi-normal modes and scrambling rates, and the modular-flow structure in black hole entanglement wedges. Combining these results with multi-band gravitational-wave predictions yields an observationally allowed region in the R-layer parameter space, establishing a controlled bridge between quantum information geometry and black hole phenomenology.