A Basis-Sensitive Companion to Spectral Dimension: Heat-Kernel Concentration Observables for Diffusion Geometry

This preprint introduces basis-sensitive coherence observables for self-adjoint generators and benchmarks them against spectral dimension, disorder localization, and modular-Hamiltonian structure. The results show that the proposed observables capture operator structure not visible to eigenvalue-only diagnostics and can distinguish modular architectures even when entanglement entropy is nearly matched.