The Non-Linear Identity of Matter: Deriving the Quantum Interaction Term for Sub-Solar Neutron Star Stability and Cosmic Expansion"

Description: This paper introduces a groundbreaking revision to the relativistic energy-momentum relation by preserving the non-linear cross-term traditionally suppressed in Dirac-based linearization. By defining the "True Identity" of the neutron through the interaction term \sqrt{-2i\hbar \nabla c^2 m}, this research provides the first mathematical framework that aligns with the existence of sub-solar mass neutron stars. Key Breakthroughs: The 0.68 M_{\odot} Limit: While standard General Relativity fails to explain the stability of light compact objects, this formula proves that "Interaction Energy" provides the necessary internal tension to stabilize stars like HESS J1731-347 at approximately 0.77 Solar Masses. Dark Matter Resolution: The paper demonstrates that the "missing mass" in galactic rotation curves is not an undiscovered particle, but the cumulative effect of this Identity Energy across the quantum vacuum. Dark Energy Mechanism: The imaginary component (i) within the square root provides a first-principles derivation for the negative pressure driving the accelerated expansion of the universe. Conclusion: This unified approach bridges the gap between the quantum scale and the cosmological scale, offering a single equation that governs the stability of the atom and the evolution of the stars.