Boundary-Driven Fractal Generation Mechanism: From Time Scale Mother Ruler to Feedback Scattering and Critical Interfaces
Boundary-Driven Fractal Generation Mechanism: From Time Scale Mother Ruler to Feedback Scattering and Critical Interfaces
Within unified boundary--time--scattering framework, analyze widespread ``fractals grow on boundaries'' phenomenon in nature. Provide rigorous characterization from three complementary threads: (i) On total space Y=M\times X^\circ of manifold with boundary and parameter space, take time scale mother ruler \kappa(\omega)=\varphi'(\omega)/\pi=\rho_{rel}(\omega)=(2\pi)^{-1}trQ(\omega), relative topological class [K]\in H^2(Y,\partial Y;Z_2), scattering family K^1 class [u]\in K^1(X^\circ) as fundam
- National University of Singapore Singapore
General Relativity, Modular Flow, Unified Time Scale, Information Theory, Boundary Time Geometry, Wigner-Smith Time Delay, Causal Structure, QNEC, Quantum Scattering, Generalized Entropy, Spectral Shift Function, Time Geometry
General Relativity, Modular Flow, Unified Time Scale, Information Theory, Boundary Time Geometry, Wigner-Smith Time Delay, Causal Structure, QNEC, Quantum Scattering, Generalized Entropy, Spectral Shift Function, Time Geometry
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