FUEMSₘsd Model: A Unified Finite Universal Energy-Mass Singularity Framework

The standard ΛCDM model leaves two fundamental problems unsolved: the initial singularity (infinite density and curvature) and the physical origin of dark energy. The FUEMSₘsd model (Finite Universal Energy-Mass Singularity - Mashudur Rahman version) resolves both by postulating that (i) the total energy of the universe is finite and constant, and (ii) spacetime is an elastic medium with a maximum curvature limit. The model replaces the classical singularity with a pre-singularity state - a finite, non-zero Planck volume, timeless (dt/dτ = 0), yet quantum-active (ΔEΔt ≥ ħ/2) configuration where all energy is stored as elastic potential energy of the spacetime fabric. A three-effect feedback loop (Quantum Confinement Frustration, Elastic Limit Saturation, Quantum Tunneling with Back-Reaction) triggers the Big Bang when the outward quantum kick overcomes the elastic snap-back. After the Big Bang, the fabric gradually releases its stored energy, which appears as dark energy. The stored energy decreases, but the dark energy density remains nearly constant today because the expansion volume grows. When the stored energy falls below a critical threshold, the fabric undergoes a sudden phase transition - dark energy vanishes abruptly, producing an inertial shock that accelerates the disintegration of all structures. This Kinetic Dissolution proceeds through seven levels (from galaxy clusters down to the spacetime metric itself), ending with gμν → 0 and dt/dτ → 0. The model eliminates infinities, respects energy conservation, and makes falsifiable predictions (CMB cutoff at ℓ ~ 10⁴, sudden future deceleration). This paper presents the complete mathematical formulation, physical interpretations, and comparisons with ΛCDM.