The Bekenstein-Einstein Bridge: Deriving Mass-Energy Equivalence from the Computational Limits of the Spatial Manifold

For over a century, the mass-energy equivalence equation E=mc² has been fundamentally understood through the lens of special relativity. Under the Informational Constraint Framework (ICF), we demonstrate that Einstein's equation can be derived entirely from information theory and thermodynamic geometry without requiring relativistic postulates. By substituting the quantum geometric footprint of localized spatial strain (the reduced Compton wavelength) directly into the Bekenstein bound, we mathematically demonstrate that "mass" is not an intrinsic physical material. Instead, mass is a highly localized 2π topological knot of frozen informational strain within the continuous spatial manifold. Echoing John Archibald Wheeler's "It from Bit" paradigm and Landauer's Principle of information erasure, E=mc² naturally emerges as the precise thermodynamic conversion rate detailing the computational exhaust released when this spatial geometry is forced to unfold. Open-Science Artifacts Included in this Repository: BekensteinEinsteinBridge. pdf: The primary theoretical manuscript detailing the algebraic derivation. ICFMassKnotEngine. py &. ipynb: The reproducible Python codebase used to mathematically map and generate the 3D geometry of the mass singularity. TheTopologicalKnotPrint. png: The high-DPI publication-ready artifact generated by the engine. TheTopologicalKnotCinematic. mp4: A narrated visual master-cut serving as an accessible cinematic entry point to the phase-space geometry. README. md: The visual decoder key explaining the topological features.