Algorithmic Data Compression in Emergent Spacetime: Resolving the Black Hole Information Paradox via Thermodynamic Graph Dynamics

The black hole information paradox has resisted resolution for half a century, trapped between general relativity's inescapable event horizons and quantum mechanics' strict demand for unitarity. This paper resolves the paradox within the Algorithmic Theory of Reality (ATR) by reframing spacetime not as a fundamental continuous fabric, but as a dynamically allocated, finite-bandwidth data structure. We demonstrate that an event horizon is fundamentally an algorithmic information boundary. When a local region's data density (mass) exceeds the observer's holographic processing capacity governed by the Bennett-Landauer bound, the system prevents a local rendering crash by compressing the interior data and routing it into an unrendered backend (the Singleton). Information is never destroyed; it is simply processing-disconnected from the 3D spatial sub-state. Key Results: Holographic Overflow: The mathematical identity between the Bekenstein information bound and Bekenstein-Hawking entropy at the Schwarzschild radius (rs) is reinterpreted as a strict computational bandwidth saturation condition. Hawking Radiation as Data Decompression: We prove that the Hawking temperature (TH) is thermodynamically consistent with the Bennett-Landauer bound. Each Hawking quantum represents the decompression of exactly one nat of information at the absolute minimum energy cost (kBTH). Global Unitarity & The Page Curve: Information conservation is guaranteed globally by the static Singleton state. The Page curve naturally emerges as the statistical signature of this bipartite decompression protocol. Scale Unification: The exact same thermodynamic limit that governs Dark Energy and the MOND acceleration scale is shown to dictate the formation of black hole event horizons. Computational Verification: The paper is accompanied by a dynamic spatial graph network simulation. By simply enforcing a strict processing bandwidth limit on network nodes, the simulation spontaneously forms an isolated clique (an event horizon), demonstrates the Bekenstein-Hawking Area Law (S ∝ A), and qualitatively reproduces the Page curve—all without programming any explicit gravitational physics. Supplementary Code: The pure Python verification script reproducing the graph dynamics is available open-source at: https://github.com/srdrymn/atr-resolving-black-hole-information-paradox