Spectral Reconstruction of Spacetime: Testable Gravitational Jitter from Quantum Entanglement

We demonstrate that the Einstein field equations emerge from the spectral properties of a quantum entanglement network. By utilizing a self-adjoint discrete Dirac operator, we recover emergent distances and demonstrate negative Ollivier-Ricci curvature in entanglement-deficit regions. We derive a non-singular cosmological bounce induced by Turán graph saturation at ρc ≈5.1 ×1093 g/cm3 and predict a fundamental 1/f gravitational jitter with amplitude h(f)∼10−21 Hz−1/2 , testable with LISA within the next decade.我们证明，爱因斯坦场方程可由量子纠缠网络的谱特性导出。通过采用自伴离散狄拉克算子，我们得到了涌现距离，并验证了纠缠亏损区域内存在负奥利维尔-里奇曲率(Ollivier-Ricci curvature)。我们推导得到由图兰图(Turán graph)饱和诱导的无奇点宇宙反弹，其临界密度ρ_c≈5.1×10^93 g/cm³，并预言了一类基础的1/f型引力抖动，其振幅满足h(f)~10^−21 Hz^−1/2，该信号可在未来十年内通过激光干涉空间天线(Laser Interferometer Space Antenna, LISA)开展探测。