SDRIS: The Geometric Origin of Special Relativity – Recovering the Speed of Light, Time Dilation, and E=mc² from Unitary Graph Dynamics (Series: Paper 104)

Special Relativity is conventionally understood as a geometric property of a continuous spacetime manifold. In this paper, we recover its fundamental laws—the causal speed limit ($c$), time dilation, and the energy-momentum relation—strictly from the information-theoretic axioms of the Static-Dynamic Recursive Information Space (SDRIS).

Instead of postulating $c$, we derive it as the Lieb-Robinson Bound of the discrete vacuum graph, representing the maximum propagation velocity of causal influence in a local network. We demonstrate that Time Dilation is not a geometric axiom but a consequence of Unitarity: The conservation of probability density forces a trade-off between spatial translation and internal state evolution (Quantum Walk dynamics).

Furthermore, we show that Length Contraction arises from the failure of global simultaneity in sequential updates ("Scan-Line Artifact"). Finally, we discard the concept of relativistic mass and derive $E=mc^2$ from the invariant norm of the information 4-flux vector. We conclude that Minkowski spacetime emerges as the hydrodynamic limit of a unitary, discrete cellular automaton operating at the Planck scale.

Includes:

• Full mathematical derivation.

• Python simulation code (SDRIS_104_Simulation_Relativity.py) visualizing the unitarity constraint ($v^2 + v_{time}^2 = c^2$).