Beyond the Boundary: A Dimensional-Constraint Extension of Mass-Energy Equivalence under Quantum Fluctuations and Topological Elasticity

As the foundational pillar of modern physics, E = mc^2 successfully governs macroscopic relativistic mechanics. However, in regimes characterized by extreme quantum fluctuations, topological constraints, and multidimensional boundary conditions, the traditional energy-momentum relation requires an elastomeric extension. This paper proposes a generalized theoretical framework, introducing a "Dimensional-Constraint Energy Correction" (Δ EDC) governed by topological boundary parameters (Λ_i) and Bethe-string interaction dynamics (Bstring). Crucially, Δ EDC is not an arbitrary ad-hoc modification, but a mathematical necessity reflecting the elastomeric response of space-time—acting as a robust structural "axis" that absorbs quantum uncertainties. To bridge microscopic fluctuations with macroscopic spacetime, a topological field integration is introduced. Rather than superseding Einstein’s formulation, this model incorporates it as a limiting boundary condition (Δ EDC → 0), offering a resilient bridge between microscopic strings and macroscopic spacetime. This work is presented as an open collaborative model, welcoming global independent research contributions.