This work demonstrates coherent spectral activation determines effective dimensional behavior in physical systems, implying new insights into dimensional emergence.
Key Points
The aim is to define effective dimension from an operational perspective through spectral observables.
Utilized heat-trace and diffusion diagnostics with self-adjoint operators.
Analyzed dimensional behavior based on scale-dependence and spectral gap structure.
Identified crossover scales contributing to observable dimensional dynamics.
Observed that dimensional behavior can emerge through ordered spectral activation.
Established that discrete plateaus in spectral dimension result from this activation.
Demonstrated robustness against perturbations, negating the need for fine-tuning.